Question

Derek will deposit $3,768.00 per year for 13.00 years into an account that earns 13.00%. Assuming the first deposit is made 6.00 years from today, how much will be in the account 37.00 years from today?

Answer 1

FV of Annuity = P*[{(1+i)^n}-1]/i

Where, P = Annuity = 3768, i = Interest Rate = 0.13, n = Number of Periods = 13

Therefore, FV = 3768*[{(1+0.13)^13}-1]/0.13= 3768*3.898/0.13 = 112982.35

Above FV is 13 years from 6 years from now i.e. 19 years from now.

Therefore, to find FV 37 years from today, we need to calculate the FV of above amount after 37-19 = 18 years

FV = PV*[(1+i)^n]

Where, PV = 112982.35, i = 0.13, n = 18

Therefore, FV = 112982.35*[(1+0.13)^18] = 112982.35*9.024268 = 1019583

Therefore, Account Balance 37 years from today = $1019583