Question

a. Suppose you wanted to know in todays value how much money your grandparents earned each year. If your grandparents earned $3000 per year in 1954 and the inflation rate on average is 2%, how much would this $3000 be worth in 2020?

b. Suppose you have 2 alternative investments. Investment 1 is very safe; you can invest $1000 at a rate of 2% for the next 10 years. Investment 2 is very risky; you can invest your $1000 at a rate of 8%; however, there is a 50/50 chance you will receive nothing in the end. Which investment do you chose and why?

c. Suppose you are interested in purchasing an asset that costs $60,000, but you currently only have $45,000. If you can earn 6% compounded semi annually, how long will it take until you can afford to purchase the asset?

Answer 1

a . Amount in 2020 = Future value = Present value * ( 1 + interest rate )^ no of years

= 3000 * 1.02^66 = 11084.92

3000 be worth $11084.92 in 2020 .

b.

Future value of Investment 1 = 1000* 1.02^10 = 1218.99

Future value o investment 2 = 0.5 * 1000*1.08^10 + 0.50*0 = 1079.46

We will chose Investment 2 as it has higher expected future value

c. Future value = Present value * ( 1 + interest rate )^ no of years

60000 = 45000 * ( 1.03 ) ^2n

60000 / 45000 = 1.03^2n

1.33 = 1.03^2n

1.33^0.5 = 1.03^n

1.15 = 1.03^n

Let us use Financial calculator

PV +-45000

FV = 60000

I/ Y = 3

N = ?

CPT< N < 9.73

N of years = 9.73 /2 = 4.87 years