Jeremy invests 8000 into lrpp+2nnk6:y a savings account that pays an annual interest rate of 5.5 %, compounded annually. p 6pnl2:yrk+n

1.Write down a formula which calculates that total value of the investment after n years.
FV=x(1+y)$^n$;x=  ,y=  .
2.Calculate the amount of money in the savings account after:
2.1.
1 year;FV=  .
2.2.
3 years.FV≈  .

3.Jeremy wants to use the money to put down a $10000 deposit on an apartment. Determine if Jeremy will be able to do this within a 5-year timeframe. ----待选择----yesno 

  In this question give all answerad(,n9q-q .zg r lgo5ys correct to two decimal places.

Mia deposits 4000 Australian dollars (AUD) into a bank account. The bank pays a nominal annual interest rate of 6 %, compounded semi-annually.

1.Find the amount of interest that Mia will earn over the next 2.5 years.

Ella also deposits AUD into a bank account. Her bank pays a nominal annual interest rate of 4 %, compounded monthly. In 2.5 years, the total amount in Ella's account will be 4000 AUD.

2.Find the amount that Ella deposits in the bank account.
PV≈   AUD

  Maria invests 25000 into a savings account that pays a nominal annual intebw3c.ifk +qt1 91mutzw/2xn /t7 jhysrest rate of 4.fs tn th y.x119k/uc/q3+z2m7twjwbi25 %, compounded monthly.

1.Calculate the amount of money in the savings account after 3 years.
FV≈  .
2.Calculate the number of years it takes for the account to reach 40000.
Hence it takes    yearsfor the account to reach 40000.

  Hannah buys a car for 24900. The value of the car depreciates by 16 % each yb*zf)i o,vhf-/e1bhd 6jf* ckear. bh*ib)/c 6,-z *vffhdj ef1ok

1.Find the value of the car after 10 years.
FV≈  .

Patrick buys a car for 12000. The car depreciates by a fixed amount each year, and after 6 years it is worth 6200.

2.Find the annual rate of depreciation of the car.
r≈  %

  In this question give alo9n- fs:hwzfh b0;zy 9l answers correct to two decimal places.

Elena invests in a retirement plan in which equal payments of €1500 are made at the beginning of each year. Interest is earned on each payment at a rate of 2.49 % per year, compounded annually.

Find the value of the investment after 25 years.
Hence the value of the investment after 25 years is €=  .

Find the amount of interest Elena will earn on the investment over 25 years.
The amount of interest earned on the investment over 25 years is=€  .

  Edward wants to buy a /s q/+dc7b we1why. aynew car, and he decides to take out a loan of 70000 Australian dollars from a bank. The loan is for 6 years, with a nominal annual interest rate of 7.2%, compounded monthly. Edward will pay the loan in fixe+.7aybcywhs ew1// qdd monthly instalments.

1.Determine the amount Edward should pay each month. Give your answer to the nearest dollar.
Hence Edward should pay    each month.
2.Calculate the amount Edward will still owe the bank at the end of the third year.
Therefore the outstanding balance is   
​

  Isabella and Charlotte both receives 80000 Australian dollarnc iolot3)l3:v k//hfs (AUD) on their 18t/v):knc3/ l 3t oihlfoh birthday to invest for later in their life.

Isabella deposits her 80000 AUD in a bank account that pays a nominal annual interest rate of x %, compounded monthly.

1.The amount in a bank account after 6 years will be 100000 AUD. Find the nominal annual interest rate. Give your answer correct to two decimal places.
x≈  %
Charlotte uses her 80000 AUD to buy a house that increases in value at a rate of 3 % per year.

2.Find the house price after 6 years.
FV≈  AUD

  In this question give all answers correct to two decima0vvznq.t2e9y p vgd)l3sg1q3ng p70k l places.

Charlie deposits 8000 Canadian dollars (CAD) into a bank account. The bank pays a nominal annual interest rate of 5 %, compounded semi-monthly.

1.Find the amount of interest that Charlie will earn over the next 2 years.

Oscar also deposits CAD into a bank account. His bank pays a nominal annual interest rate of 6 %, compounded quarterly. In 2 years, the total amount in Oscar's account will be $8000 CAD.

2.Find the amount that Oscar deposits in the bank account.
PV≈  CAD.

  Ali bought a car for 18000. Th6z+ .bthbbw p-dol0x5 e value of the car depreciates by 10.5 % each year.hz+txpwdl. b5bb-06o

1.Find the value of the car at the end of the first year.
FV≈  .
2.Find the value of the car after 4 years.
FV≈  .
3.Calculate the number of years it will take for the car to be worth exactly half its original value.
n≈  years.

  Benjamin spends € 32000 buyicwh1i)q2yg g-g6: it ong bitcoin mining hardware for his cryptocurrency mining business. The hardware- 6qg oiig:)ywctg 12h depreciates by 16 % each year.

1.Find the value of the hardware after two years.
FV≈€   .
2.Find the number of years it will take for the hardware to be worth less than €8000.
Hence it takes    years for the hardware to be worth less than

  In this question give all answers correct to two decim;2c-zhxqu8 ( l/jntmial places.

George invests in a retirement plan in which equal payments of 2750 are made at the end of each year. Interest is earned on each payment at a rate of 3 % per year, compounded semi-annually.

1.Find the value of the investment after 20 years.
Hence the value of the investment after 20 years is   .
2.Find the amount of interest George will earn on the investment over 20 years.
The amount of interest earned on the investment over 20 years is   .

  Charles plans to invest in a retirement plan for 30 years. In this plan, he wir9lt0xo9hm,wt ay1 2k ll deposit 1000 British pounds (GBP) at the end of every month and receive a 6lx,h2k yot ra0 9tw9m1.5% interest rate per annum, compounded monthly.

1.Find the future value of the investment at the end of the 30 years. Give your answer correct to the nearest pound.
Hence the value of the investment at the end of the 30 years is   GBP.
After the 30-year period, Charles will start receiving regular monthly payments of 1500 GBP.

2.Calculate the number of years it will take Charles's monthly retirement payments to match the total amount originally invested.
Hence Charles breaks even with the amount he invested after   years.

  At the beginning of each year, Jack invests h:6qog *inul4 5000 in a savings account that pays 4% ni u6q:g* 4lhoannual interest, compounded quarterly

1.Find the number of years it will take until Jack has 100000 in his account.
Hence it will take    years until Jack has 100000 in his account.
At the beginning of each year, John invests 6000 in a savings account that pays an annual interest rate, compounded semi-annually. After 20 years John has 200000 in his account.

2.Find the annual interest rate.
Hence the annual interest rate is   %
​

  Alex invests an amount of;ush- zr/9xntosa1 d b/x0 vd7 USD into a savings account which pays 3.3% (p.a.) interest, compounded monthly. Af b/0d1d/xvs9u rz;n-t7x ao shter 5 years Alex has 8000 USD in the account.

1.Find the amount of USD initially invested, rounding your answer to two decimal places.

With this money, Alex purchases a used car for 5000 dollars, and sells it 3 years later for 4200.

2.Find the rate at which the car depreciates per year over the 3 year period.
We can use the compound depreciation formula to solve for r=  .

  Michael buys a second hand Tesla caq t yyn84sta;5r for $18000. The value of the car depreciates by 10% each year.

1.Find the total amount the car will depreciate after 5 years, giving your answer correct to the nearest dollar.

The price of a different used car depreciates by 5% each year.

2.Find the value reduction of this car after 4 years as a percentage, when compared to the original purchase price.
Hence, the reduction in price after 4 years as a percentage is =  %

  Mike wants to deposit part of his savings in ak*/:hftdhle 4 bank account that pays an annual interest rate * /:dthfelh4 kof 4.1% compounded annually. The annual inflation rate is expected to be 3% per year throughout the following 8 years. Mike wants his initial deposit to have a real value of 5000 after 8 years, compared to current values.

The bank gives Mike two proposals: 
Proposal 1:A one-time investment at the start of the 8-year period.

Proposal 2:Invest 2000 at the start of the 8-year period and make payments of $ x at the end of each year.

1.Find the minimum amount Mike should deposit if he accepts proposal 1. Round your answer to the nearest dollar.

2.Find the minimum value of the annual payments, x, if Mike accepts proposal 2. Round your answer to the nearest dollar.
Hence the amount Mike should pay each year is   .
​

  Greg has saved 2000 British pounds (GBP) over the lasw udkcdhd 06 jzrsj-ba58y3h8)h; kd.t six months. He decided to deposit his savings in a bank which offers a nominal an. h chrk5w;bd386 dya-8dzkuh )sjj0dnual interest rate of 8%, compounded monthly, for two years.

1.Calculate the total amount of interest Greg would earn over the two years. Give your answer correct to two decimal places.
Hence, using the compound interest formula, we get   GBP; Hence the total amount of interest earned is   GBP.
Greg would earn the same amount of interest, compounded semi-annually, for two years if he deposits his savings in a second bank.

2.Calculate the nominal annual interest rate the second bank offers.
Hence, using the compound interest formula, we obtain r≈  %.

  Smith has saved $5000 from working a part-time job and wants to invest this money so that it grows over time. His bank offers a savings account that pays an annual interest rate of 4.2%, compounded quarterly.

1.Find how many years it will take for Smith's investment amount to double in value, rounding your answer to the nearest integer.
n=  .
Smith wants his money to grow faster than this first option. His wants to invest the money so that it will double in value in 5 years. He considers an high-growth, higher-risk option, which pays an annual interest of r%, compounding half-yearly.

2.Determine the value of r required in this option, rounding your answer to two decimal places.
r=  %.

  Emily deposits 2000 Australian dollars (AUD) intrj3+40d myab e:wkd4 v(nkxm, o a bank account. The bank pays awbkekad4 my3, r x4v nd(m0+:j nominal annual interest rate of 4 %, compounded monthly.

1.Find the amount of money that Emily will have in her bank account after 5 years. Give your answer correct to two decimal places.
FV=  AUD.
Emily will withdraw the money back from her bank account when the amount reaches 3000 AUD.

2.Find the time, in full years, until Emily withdraws the money from her bank account.
n≈  .

  In this question give all answers correct to the nearest whole numbe2el9:qx s8 zmd3ypoa+5i pyk 2r.

Michelle takes out a loan of $12000. The unpaid balance on the loan has an interest rate of 4.3 % per year, compounded annually.

1.The loan is to be repaid in payments of $1500 made at the end of each year.
Hence it will take    years to repay the loan.
1.1.Find the number of years it will take to repay the loan.

1.2.Calculate the total amount that has been paid in amortising the loan.

2.The loan is to be amortised over 5 years.

2.1.Find the annual payment made at the end of each year.
Hence the annual payment is   .
2.2.Calculate the total amount that has been paid in amortising the loan.
The total amount that has been paid in amortising the loan is ≈  .

  In this question give all answers correctp 8wom1yut ).h to two decimal places.

Stella receives a loan of € 32000 for her flower shop business at an interest rate 5.29 % per year, compounded monthly. She agrees to pay back the loan in 60 equal installments, made at the end of each month over the next five years.

1.Calculate the amount of monthly installment.
Hence the amount of monthly installment is €  .
Four years after she starts repaying the loan, Stella decides to repay the rest in a final single installment.

2.Calculate the amount owing at the end of the four years.
Hence the amount still owing at the end of the four years is €  .
​

  Julia wants to buy a house that requires a depo lkb 4,qla6,i4 wsww/ s1xk))auehub1 2 uilg1sit of 74000 Australian dollars (AUD).4),w1wu6 b1, ea )ahllsb4 xk /iqwl1ukgsiu2

Julia is going to invest an amount of AUD in an account that pays a nominal annual interest rate of 5.5 %, compounded monthly.

1.Find the amount of AUD Julia needs to invest to reach 74000 AUD after 8 years. Give your answer correct to the nearest dollar.
Hence, using the compound interest formula, we get PV≈  AUD.

Julia's parents offer to add 5000 AUD to her initial investment from part (a), however, only if she invests her money in a more reliable bank that pays a nominal annual interest rate only of 3.5 %, compounded quarterly.

2.Find the number of years it would take Julia to save the 74000 AUD if she accepts her parents money and follows their advice. Give your answer correct to the nearest year.
Hence it would take Julia    years to save the 74000 AUD.

  Olivia takes a mortgage (loan) of 250000 to buy an ap 5gd1gi ,q 5u/ym tt3t8zd1p*q9eyjqgartment in Sydney. Interest on the loan accumulates at the rate etdqyg9gydim/5q35 j*q18,1 g t ptz uof 3.49 % per year, compounded semi-annually. Olivia agrees with the bank to amortise the loan in monthly payments, made at the beginning of each month.

1.Given that the loan is to be amortised over 30 years, find:

1.1.the monthly payment amount;
Hence the amount of monthly payment is   .

1.2.the total amount paid in amortising the loan.
The total amount that has been paid in amortising the loan is≈  .

2.Olivia has the capacity to increase her monthly payments by $85. Justify to Olivia why this may be a smart financial choice.
Olivia will save (≈)  years.

  Phil's phone shop sells Azura smartphones foq rb*tt8sk bnk*d*f1(b-cbl vw0 m7v-r $1499 and Bellson smartphones for $850. It is expected that a Bellson smartphone will depreciate at a rate of 20% per year.

After 2 years, an Azura smartphone is worth approximately $735.

1.Show that the expected annual depreciation rate of an Azura smartphone is 30%.2
Hence, using the compound depreciation formula, we get r=  %.

An Azura smartphone and a Bellson smartphone will have the same value n years after they were purchased.

2.Find the value of n.
Hence, using the compound depreciation formula, we obtain n ≈  .
3.Comment on the validity of your answer to part (b).

  Bruce goes into a car dealership to purchase a new vehicle. The one he wantsgyklvhb-:qco0c)n/ i xb: +b9 to buy costslbi +b)/kngxvyoh :-b c 90qc: 16000, however he doesn't have that much money in his bank. The salesman offers him a financing option of a 30 % deposit followed by 12 monthly payments of 1150.

1.Find the amount of the deposit.
The amount of the deposit is PV=  .
2.Calculate the total cost of the loan under this financing option.
The total cost of the loan is FV=  .
Bruce's father generously offers him an interest free loan of

16000 to buy the car to avoid the expensive loan repayments. They agree that Bruce will repay the loan by paying his father $x in the first month and y every following month until the 16000 is repaid.
The total amount Bruce's father receives after 12 months is 5200. This can be expressed by the equation x+11y=5200. The total amount that Bruce's father receives after 24 months is 10600.

3.Write down a second equation involving x and y.
x+  y=  
4.Determine the value of x and the value of y.
X=  ; Y=  .
5.Calculate the number of months it will take Bruce's father to receive the 16000.
N=  .
Bruce decides to buy a cheaper car for 12000 and invest the remaining $4000. He is considering two investment options over four years.

Option A: Compound interest at an annual rate of 6.5 %.
Option B: Compound interest at a nominal annual rate of 6 %, compounded monthly.

Express each answer in part (f) to the nearest dollar.

Calculate the value of each investment option after four years.

6.1.Option A.
Hence, using the compound interest formula, we get FV≈  .
6.2.Option B.
Hence, using the compound interest formula, we obtain FV≈  .

  Ray takes out a loan ofz k8-*tv6ks3ves5rxs v ei -+g $200000 to purchase a house. He agrees to pay the bank $1250 at the end of every month to amortise the loan, and interest accumulates on the balance at a rate of 3.79 % per year, compounded monthly.

1.Find the number of years and months it takes to pay back the loan.
Hence it takes    years and    months
18 years and 8 months to pay back the loan.
2.Calculate the total amount that Ray has paid in amortising the loan.

3.Ray decides to increase the monthly payment to $1500. Justify this decision.

  Tom takes out a loan ofz:p4 m foujnmq fv(wi5f6r 3/, $80000 to purchase some new machinery for his farming business. He agrees to pay the bank $1200 at the end of every month to amortise the loan. Interest accumulates on the balance at a rate of 5.65 % per year, compounded monthly.

1.Find the number of years and months it takes to pay back the loan.
Hence it with take    and    months to pay back the loan.
2.Calculate the total amount that Tom pays in amortising the loan.

3.Tom decides to increase the monthly payment to $1500. How much interest will Tom save in comparison to the former payment schedule.

  Nathan receives a lump sum inheritance of 55000 and invests the monz.h7 2wnw:y; 8-xex uolr+m sgey into a savings accoun w.28:ely mo;7 n wugxhsz-rx+t with an annual interest rate of 7.5%, compounded quarterly.

1.Calculate the value of Nathan's investment after 5 years, rounding your answer to the nearest dollar.3After m months, the amount in the savings account has increased to more than 70000.
FV=  .
2.Find the minimum value of m, where m∈N.
m=  months.
Nathan is saving to purchase a property. The price of the property is 150000. Nathan puts down a 15% deposit and takes out a loan for the remaining amount.

3.Write down the loan amount.
The loan duration is for eight years, compounded monthly, with equal monthly payments of 1500 made by Nathan at the end of each month.
Loan amount=  .
4.For this loan,
4.1.findthe amount of interest paid by Nathan over the life of the loan.
Interst paid=  .
4.2.the annual interest rate of the loan, correct to two decimal places.
The annual interest rate of the loan is   %
After 5 years of paying this loan, Nathan decides to pay the outstanding loan amount in one final payment.

5.Find the amount of the final payment after 5 years, rounding your answer to the nearest dollar.
The final payment after 5 years is(≈)   .
6.Find the amount Nathan saved by making this final payment after 5 years, rounding your answer to the nearest dollar.
Amount saved=  .

  Lily and Eva both receive 50000 Australian dollaugew98 c*ol; hrs (AUD) on their 18th birthday. Lily deposits her 50000 AUD into a bank account. The bank pays an annual interest rate of 5 %, compounded yearly. Eva invests her 50000 AUD into a he o*;gcwu8 hl9igh-yield mutual fund that returns a fixed amount of 3000 AUD per year.

1.Calculate:

1.1.the amount in Lily's bank account at the end of the first year;
Hence, using the compound interest formula, we get FV=  AUD.
1.2.the total amount of Eva's funds at the end of the first year.
We have FV=  .
2.Write down an expression for:

2.1.the amount in Lily's bank account at the end of the nth year;
Hence, using the compound interest formula, we obtain FV=x(1+y)$^n$.x=  ,y=  .
2.2.the total amount of Eva's funds at the end of the nth year.
We have FV=50000+(x)n.x=  .
3.Calculate the year in which the amount in Lily's bank account becomes
greater than the amount in Eva's fund.
Hence this will happen in   th year
​
4.Calculate:

4.1.the interest amount that Lily earns if invested for 12 years, giving your answer correct to two decimal places;

4.2.the amount of funds that Eva earns for her investment if invested for
12 years.

  Ann is considering i1upmmsvb5i 4c n/uof1*hs- c.nvesting $85000 into a term deposit in one of two banks. The first bank offers an annual interest rate of 3 %, compounding monthly. The second bank offers a fixed payment amount of 250 per month.

1.Calculate:

1.1.the amount that would be in the account in the first bank at the end of the first year;
Using the compound interest formula, we get FV(≈)   .
1.2.the amount that would be in the account in the second bank at the end of the first year.
We have FV=  .
2.Write down an expression for:

2.1.the amount in the account in the first bank at the end of the nth year;

2.2.the amount in the account in the second bank at the end of the nth year.

3.Calculate the year in which the amount in the first bank account becomes
greater than the amount in the second bank.
Hence this will happen in   th year
4.Calculate:

4.1.the interest that Ann would earn if she invested in the first bank for 10 years;

4.2.the interest that Ann would earn if she invested in the second bank for 10 years.
Hence the amount of interest earned in the second bank is