Question

7. (EAR and Nominal Interest Rate) An investment will increase in value by 270% over the next 17 years. What is the annual interest rate which, when compounded quarterly, provides this return?

8. (Perpetuity)A firm invests $3 million in a project which will yield a perpetuity of $1 million per year. What is the discount rate r for which this project’s present value is $4.5 million?

9. (Amortization) You just bought a car with loan of $50,000. You have to repay the loan in 6 years with monthly payments. The interest rate on the loan is 4%. a. What is your monthly payment? b. How much will you still owe after 4 years? (i.e. what is the loan balance after 4 years?)

Answer 1

7. FV = PV ( 1+r/4)^4*17

Or, 1+ 2.70 = (1+.25r)⁶⁸

Or, 1+0.25r =

Or, 1.025r = 1.0194

r= 7.76%

8. PV = CF_P/(1+r)ⁿ

4.5 million = 1/(1+r)ⁿ

Or, (1+r)ⁿ = 1/4.5 = 0.22 or 22%

9. The formula for monthly payment is

Or, A =

Or, A = 50,000 x (0.00386539/0.171329)

Or, Monthly payment = $1,128

Now, solving for remaining balance

FV = PV(1+r)ⁿ -

Or, FV = 50,000(1+0.0033)⁷² -  

Or, FV = 63,385.29 - 58,566.56 = $4,818.73