Question

It is now January 1, 2001. You plan to make only 5 deposits of $500 each, one every 6 months, with the first payment being made today. If the bank pays a nominal interest rate of 10%, but uses semiannual compounding, how much will be in your account after 5 years?

Answer 1

Compounding frequency = 2 (As the compounding will be done semi annually i.e. two times a year)

So Rate of interest used = 10%/2 = 5%

Balance where

Time Opening Balance Annual Payment interest to be applied Interest Closing Balance

(A) (B=F) (C)    D=B+C E F=D+E

Y1 T0 - 500 500 500*5%=25 525

Y1 T1 525 500 1025 1025*5%=51.25 1076.25

Y2 T0 1076.25 500 1576.25    1576.25*5%=78.81 1655.06

Y2T1 1655.06 500    2155.06    2155.06*5%=107.75 2262.81

Y3T0 2262.81 500 2762.81 2762.81*5%=138.14   2900.95

Y3T1 2900.95 - 2900.95    2900.95*5% = 145.05 3046

Y4T0 3046 - 3046 3046*5%=152.30 3198.30

Y4T1 3198.30 -    3198.30 3198.30*5%= 159.91 3358.21

Y5T0 3358.21   -    3358.21    3358.21*5%= 167.91 3526.13

Y5T1 3702.44 -    3526.13 3526.13*5%= 176.31   3702.44

So the amount after 5 years in the account will be $3702.44