Question

Interest rate. In​ 1972, Bob purchased a new Datsun 240Z for ​$2,500. 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?

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

Answer 1

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

Bob purchased Dastun car in 1972 for = $2500

In 2002 he could sell car for 6 times the price originally paid= $2500*6

= $15000

a). Calculating Bob's annualized rate of return for the 30 years he owned this​ car:-

Annualized rate of return = (Car price today/Car purchase price)^(1/n) - 1

where, n= no of years = 30

Annualized rate of return = ($15,000/$2500)^(1/30) - 1

= 1.061545 -1

Annualized rate of return = 6.1545%

b). Bob keeps the acr for another 30 years and earns same Annualized rate of return.

calculating the Value of car in 2032:-

where,

r = Annualized rate of return = 6.1545%

n = no of years = 30

Current Value = $15000

= $15000*6.000

= $90,000

So, the price he could sell the car for in​ 2032 is $90,000

If you need any clarification, you can ask in comments.     

If you like my answer, then please up-vote as it will be motivating