Question

You deposit $175 semi-monthly (that's twice per month) into an account earning 5% interest. You play to continue the same deposit until your retirement, in 30 years.

a) How much will you have in the account after 30 years?

b) How much total money will you put in the account?

Answer: 126000

c) How much total interest will you earn?

Answer 1

a)

Fund size after 30 years can be computed using formula for FV of annuity as:

FV = P x [(1+r) ⁿ – 1/r]

P = Periodic cash flow = $ 175

r = Rate per period = 5 % or 0.05/24 = 0.002083333333 semi monthly

n = Numbers of periods = 30 x 24 = 720

FV = $ 175 x [(1+0.002083333333)⁷²⁰ – 1/0.002083333333]

     = $ 175 x [(1.002083333333)⁷²⁰ – 1/0.002083333333]

     = $ 175 x [(4.474701594695 – 1)/0.002083333333]

     = $ 175 x (3.474701594695/0.002083333333)

     = $ 175 x 1667.85676545376

     = $ 291,874.93395441 or $ 291,874.93

b)

Total money deposited (or principal only) = No. of deposits x amount in each deposit

                                                                        = 24 x 30 x $ 175 = $ 126,000

c)

Total interest earned = Future value of deposits – Total money deposited

                                       = $ 291,874.93 - $ 126,000 = $ 165,874.93