Question

4. According to WSJ, friends and relatives of young Warren Buffet regularly heard him complaining that he did not want to spend $300,000 for his haircut. Back in the day, a haircut would cost Mr Buffet around $0.5. For how long do you need to compound the haircut price to justify Mr Buffet’s complaints? Give answers assuming that interest rate is 1%, 5%, and 10%. What if you use simple interest rate?

Answer 1

We need to find n such that,

FV = PV * (1 + r)^n

(1 + r)^n = FV/PV

n * ln(1 + r) = ln(FV/PV)

n = ln(FV/PV)/ln(1 + r)

r = 1%

n = ln(300,000/0.50)/ln(1 + 0.01)

n = 1,337.109803737 years

r = 5%

n = ln(300,000/0.50)/ln(1 + 0.05)

n = 272.6919484836 years

r = 10%

n = ln(300,000/0.50)/ln(1 + 0.10)

n = 139.5935351451 years

If simple interest rates are used, then

n = (FV - PV)* 100/r

r = 1%

n = (300,000 - 0.50)*100/0.01

n = 2,999,995,000 years

r = 5%

n = (300,000 - 0.50)*100/0.05

n = 599,999,000

r = 10%

n = (300,000 - 0.50)*100/0.10

n = 599,999,000 years