Question

1. Complete the following table. Number of Annual Payments or Years Present Value Interest Rate Future Value Annuity 10 $250.00 12% 20 S1,000 25 S500,000 30 S1,000,000 2. You just started working and you planned to save $5,000 every year in your retirement account. How much money will you have in your retirement account once you retire in 40 years? Your retirement account pays 4% interest rate per year. 3. You just retired with S1,000,000 savings. You'd like to receive your savings as an annuity for 20 years. If the interest rate on your account is 5%, how mach do you receive every year? 4. You have received a S10,000 loan from your bank for 10 years. If the bank charges you 5% interest, how much do you need pay back to the bank at the end of cach year: a If the loan is a discount loan. b. If the loan is an interest-only loan. c. If the loan is an amortized loan. 5. For the previous question, calculate the total amount of money that you have to pay pack to the bank in each loan payment structure. Page 1 of 3 6. The Canadian Government has once again decided to issue a consol (a bond with a never- ending interest payment and no maturity date). The bond will pay S40 in interest cach year (at the end of the year) but never returm the principal. The current discount rate for Canadian govemment bonds is 7.5%. What should this bond sell for in the marker? 7. You want to purchase a condo in downtown Boston for S1,200,000. You can finance 80% of its cost by receiving a 20-year mortgage. Considering your income and your credit score, your bank offered 4.5% interest on your mortgage. For simplicity assume that you make yearly payments to your mortgage. Build an amortization schedule for this loan in Excel and answer the following questions. a. How much in total do you have to pay back to the bank? b. How much do you owe to the bank at the end of year 10? e. At the end of year 10, you decide to refinance your home with a new 15-year 3.5% mortgage. How much is your new yearly payment? d. Consider the initial mortgage (not the case where you refinanced). Starting from year 11, you decide to increase your yearly payments by 10% hoping that it helps you pay off your mortgage sooner. In this case, how long does it take for you to pay off your mortgage?

Answer 1

Answer to 1st Question:-

(a) Annuity = $250

Interest Rate = 6 %

Number of Years = 10

P = A(1+r/100)^n

= $250(1+6/100)^10

=$1840

(b) Interest Rate = 12

Number of year = 20

Present Value = $1000

  F = P * ([1 + I]^N - 1 )/I

= $1000*([1+0.12]^20 -1 )/.12

= $72052

(c) Present Value = $500000

Interest Rate =4 %

Number of Years = 25

P = A(1+r/100)^n

Annuity = Present Value/ [(1+r/100)^n ]

= $500000/[(1+4/100)^25]

= $32006 (approx.)

(d)  Future Value = $1000000   

Interest Rate = 2%

Number of Years = 30

  F = P * ([1 + I]^N - 1 )/I

Annuity = Future Value/[([1 + I]^N - 1 )/I]

= $1000000 / [{(1+0.02)^30-1}/0.02]

=$24777 (approx.)

Answer to 2nd Question:-

Number of year = 40

Interest Rate = 4%

Annuity = $5000

Present Value=  $5000(1+4/100)^40

= $98,963.87

Answer to 3rd Question:-

Annuity = $1000000/ [(1+5/100)^20]

=$ 80243