Question

Daniel expects to receive $4,500 at the beginning of each month for the next 10 years from the Lucy Trust. Assuming Daniel reinvests those funds the day she receives them in an investment returning 6.5%, what will she have at the end of 10 years?

Answer 1

Monthly receipts = $4,500
Period = 10 years or 120 months
Annual interest rate = 6.50%
Monthly interest rate = 0.54167%

Receipts are received at the beginning of each month.

Accumulated sum = $4,500*1.0054167^120 + $4,500*1.0054167^119 + ... + $4,500*1.0054167^2 + $4,500*1.0054167
Accumulated sum = $4,500 * 1.0054167 * (1.0054167^120 - 1) / 0.0054167
Accumulated sum = $4,500 * 169.315714
Accumulated sum = $761,920.71

So, Daniel will have $761,920.71 at the end of 10 years.