Question

Interest

rate.

In​ 1972, Bob purchased a new Datsun 240Z for

​$3,000.

Datsun later changed its name to​ Nissan, and the 1972 Datsun 240Z became a classic. Bob kept his car in excellent condition and in 2002 could sell the car for six

times what he originally paid.

What was​ Bob's annualized rate of return for the 30 years he owned this​ car?

If he keeps the car for another thirty years and earns the same​ rate, what could he sell the car for in​ 2032?

Answer 1

Question a:

Purchase Price in 1972 = $3,000

Future Value in 2002 = $3,000 * 6 = $18,000

n = 2002 - 1972 = 30 years

Let r = annualized rate of return

Future Value = Purchase Price * (1+r)^n

$18,000 = $3,000 * (1+r)^30

(1+r)^30 = 6

1+r = 1.06154492

r = 0.06154492

r = 6.15%

Therefore, annualized rate of return is 6.15%

Question b:

Value in 2002 = $18,000

n = 2032 - 2002 = 30 years

r = annualized rate of return = 6.15%

Future Value value in 2032 = Purchase Price * (1+r)^n

= $18,000 * (1+6.154492%)^30

= $18,000 *6

= $108,000

Therefore, sale value of car in 2032 is $108,000