Question

Consider the scenario where you will make semi-annual deposits (i.e. deposits are made at the end of each six month period) of $6,000 for the next five years. How much money will you have accumulated at the end of this five year period if the interest rate is:

a. [1 point] 6% compounded monthly b. [1 point] 4% compounded weekly

b. [1 point] 4% compounded weekly

Answer 1

a) effective semiannual interest rate = (1 + 6%/12)⁶ - 1 = 3.03%

Time period = 5 x 2 = 10 semiannual periods

FV = 6000 x (1 + 3.03%)⁹ + ..... + 6000 x (1 + 3.03%)⁰

FV = $ 68902.98

b) effective semiannual interest rate = (1 + 4%/52)²⁶ - 1 = 2.02%

FV = 6000 x 1.0202⁹ + ..... + 6000

FV = $ 65756.47