Question

Today, you turn 21. Your birthday wish is that you will be a millionaire by your 40th birthday. In an attempt to reach this goal, you decide to save $25 a day, every day until you turn 40. You open an investment account and deposit your first $25 today. What rate of return must you earn to achieve your goal?

		15.07%
		15.13%
		15.17%
		15.20%
		15.24%

Answer 1

amount saved every day , A = $25

period of investment in years = 40-21 = 19

period of investment in days, n = 19*365 = 6935 days

FVIFA = future value interest factor of annuity = [(1+r)ⁿ - 1]/r = [(1+r)⁶⁹³⁵ -1]/r

future value required , FV= 1 million = $1,000,000

FV = A*FVIFA = 25*FVIFA

1,000,000 = 25*FVIFA

FVIFA = 1,000,000/25 = 40,000

[(1+r)⁶⁹³⁵ -1]/r = 40,000

we have to find r by trial and error that satisfies the above equation

by trial and error we find that , r = 0.000412953

this is the rate of interest per day

Annual interest rate = 0.000412953*365 = 0.1507277 or 15.07277% or 15.07% ( after rpounding off)

hence correct option is 15.07%