Question

A rich aunt promised you $3,000 one year from today. In addition, each year after that, she has promised you a payment (on the anniversary of the last payment) that is 4% larger than the last payment. She will continue to show this generosity for 15 years, giving a total of 15 payments. If you put these payments in an account that pays 6% interest, how much will you have in this account in 15 years

Answer 1

FV = 89,342

Step-by-step explanation:

The future value of any annuity equals the sum of all the future values for all of the annuity payments when they are moved to the end of the last payment interval.

FV (Ordinary Annuity) = (C/((r-g)/100)*(1-((1+g/100)/(1+r/100))^n))*(1+r/100)^n

FV = (3000/((6-4)/(100))*(1-((1+4/(100))/(1+6/(100)))^(15)))*(1+6/(100))^(15)

FV = 89342

Where

C = First cash flow

r = interest rate

g = growth rate

n = number of payments