Question

5. If an investor wants to have $400,000 when he retires and he can earn a 6.5% annual

interest rate on his retirement account, how many years will he have to wait to retire if he
starts with $20,000 in his account?

Answer 1

The investor will have $400,000 if he waits 48 years

Explanation

It is a compound interest composed problem.

we use the formula M=C(1+r)ⁿ

where M=$400,000 C=$20,000 r=((6.5)/(100))?=0.065 n= number of years

Now we substitute in the formula 400,000=20,000(1.065)ⁿ

((400,000)/(20,000))=(1.065)ⁿ (1.065)ⁿ=20

So, if we use logarithms, we obtain log[(1.065)ⁿ]=log(20)

nlog(1.065)=log(20) then n=((log(20))/(log(1.065)))=

= ((2. 996)/(0.063))= 47. 55

The investor will have $400,000 if he waits 48 years