Question

You deposit $100 semi-monthly (twice a month) in an account earning 8% interest. You plan to continue until your retirement in 35 years.

How much will you have in your account after 35 years?

Answer 1

Annual Interest Rate = 8 % or (8/24) ~ 0.33 % per semi-month

Total Tenure = 35 years o (35 x 12 x 2) = 840 months and Amount of Deposit = $ 100

Therefore, Total Future Value of All Deposits = 100 x (1.0033)^(840) + 100 x (1.0033)^(839) + .......+ 100 x (1.0033)^(2) + 100 x (1.0033) = [{(1.0033)^(840) - 1}/{1.0033-1}] x 100 x (1.0033) = $ 453545.48 (assuming beginning of month and middle of month deposits)