Question

Question 1

Part A

What’s the present value of a perpetuity that pays $3000 per year if the appropriate interest rate is 8%?  

Part B

You set up a college fund in which you pay $3000 each year at the end of the year. How much money will you have accumulated in the fund after 8 years, if your fund earns 15% compounded annually?

Part C

What is the effective annual rate (EAR) of 6% compounded monthly?

Part D

Your bank offers you a 36-month, 3% APR car loan for a $50000 new Mercedes SLK300 Roadster. What will your monthly payment be?

Part E

You found your dream house. It will cost you $200000 and you will put down $35000 as a down payment. For the rest you get a 30-year 4.5% mortgage. What will be your monthly mortgage payment in $ (assume no early repayment)?

Answer 1

PART A

The present value of perpetuity = cash flow/interest rate

Cash flow = $3000
Interest rate = 8%
Present value = 3000/0.08 = $37,500

PART B

Amount accumulated after 8 years is calculated by finding the Future value = $41,180.46

PART C

Effective annual rate = i = ((1+r/m)^m) -1
i = effective annual rate
r = interest rate
m = number of calculations in a year

Therefore,
Effective Annual Rate = ((1+0.06/12)^12) -1 = 6.1678%

PART D

To calculate monthly payments, PMT has to be calculated = $1,454.06

PART E

To calculate monthly payments, PMT has to be calculated after deducting the down payment amount from the total amount (PV = $200,000 - $35,000 = $165,000) = $836.03