Question

Martha and Martin are 25-year-old twins. Martha makes $1,000 end-of-year payments into her investment portfolio for 10 years and makes no payments after the end of the tenth year. Martin makes no payments for the first ten years, but he makes $1,000 end of year payments starting at the end of the 11th year and continuing through the end of the 40th year. Both Martin and Martha earn 8% on their portfolios. Who will have more money at the end of the 40th year?

Answer 1

Martha:

Future value at the end of 10 years:

FV of annuity = P*[((1+r)^n - 1)/r]
P - Periodic payment = 1000
r - rate per period = 0.08
n - number of periods = 10
FV of annuity at the end of 10 years = 1000*(((1+0.08)^10 - 1)/0.08) = 14486.56

FV at the end of 40 years = PV*(1+r)^n = 14486.56*(1+0.08)^30 = $145773.31

Martin:

FV of annuity = P*[((1+r)^n - 1)/r]
P - Periodic payment = 1000
r - rate per period = 0.08
n - number of periods = 30

FV of annuity = 1000*(((1+0.08)^30-1)/0.08) = $113283.21

So, Martha has more money at the end of the 40th year