Question

Suppose you save $10,500 at the end of every six months for your retirement. If you can earn 11% per year (APR) on your investments, how much will you have saved by the time you retire in 25 years?

Answer 1

Semiannual saving = $10,500
Annual interest rate = 11.00%
Semiannual interest rate = 5.50%
Semiannual period = 50 (25 years)

Accumulated sum = $10,500*1.055^49 + $10,500*1.055^48 + … + $10,500*1.055 + $10,500
Accumulated sum = $10,500 * (1.055^50 - 1) / 0.055
Accumulated sum = $10,500 * 246.217476
Accumulated sum = $2,585,283.50

So, you would have $2,585,283.50 by the time you retire in 25 years