Exercise 1How much do you need to invest today in a CD with

Exercise 1-How much do you need to invest today in a CD with an ROR of 5.5% if you want to purchase a car 3 years from now for $10,000? Exercise 2 - Your monthly rent and living expenses are $625. How much should be put into your money market amount today, to pay for the next 12 months? Assume your money market is currently paying 5% annually. Exercise 3 - What is the ROR on an investment with the following cash flow. $50K $6K $6K is paid out at end of periods 1,2,3,4 with the investment worth $50K at end of period 4. Exercise 4 - How many years do you need to invest to obtain $100,000 at the end of year n, given that you can only invest $1500 per year? Assume 8% interest.

Solution

1) Let the investment today be worth $P. This becomes $10,000 after 3 years when invested at 5.5%. This implies we have P = 10000*(P/F, 5.5%. 3) = 10000*0.85161 = $8,561

2) To pay for next 12 installments, the money deposited now is assumed to be $P. The rate of interest is 5%. Assuming that it is compounded annually, the value of P is

P = 625(P/A, 12, 5%) = 625*8.86325 = $5,539.53

3) Let the interest (ROR) be i%. Here A is $6000 for 4 years and F is 50,000. Find i% so that

50000 = 6000(F/A, i%, 4)

This gives ROR = 51.9% using trial and error.

4) In this case, A = 1500 and F = 100,000 for r = 8%

1500 = 100,000*(A/F, 8%, n)

This gives n = 24 using trial and error.