Question

Kimberly has just started her first job and decides to begin saving for a car. She opens a savings account on October 31, 2003 with a deposit of $160, and will continue to make deposits of the same amount at the end of each month until October 31, 2006, when she will make the final deposit. If the account pays 9% interest rate compounded monthly, how much is in the account on October 31, 2009, (when Kimberly will use this money as a down payment for a car), rounded to the nearest dollar?

Answer 1

Computation of Accumulated Balance as on 31-10-2006

Deposit amount = $ 160

Interest rate = 9% Compounded Monthly

Interest rate per month = 9% /12 = 0.75%

Time period = 37 Months

We know that

Future Value of the Annuity Due = C [{ ( 1+i)^n -1}/i]( 1+i)

Here I = Interest rate per period

C-= Cash flow per period

n = No.of Payments

Future Value of Annuity Due= $ 160[ { ( 1+0.0075)^37 -1} /0.0075] ( 1+0.0075)

= $ 160[ { ( 1.0075)^37 -1} /0.0075](1.0075)

= $ 160[ { 1.31846-1} /0.0075] ( 1.0075)

= $160[ 0.31846/0.0075] ( 1.0075)

= $ 160*42.46136*1.0075

= $ 6844.77

Hence Balance as on 31-10-2006 is $ 6844.77

Computation of Balance in the account as on Oct 31,2009

We know that Future Value = Present value ( 1+i)^n

Here I = Interest rate per period

n = No.of payments

No.of Compounding period in 3 Years = 3*12 = 36 Months

Future Value = $ 6844.77 ( 1+0.0075)^36

= $ 6844.77 * ( 1.0075)^36

= $ 6844.77* 1.308645

= $ 8957

Hence Balance in the Account as on Oct 31,2009 is $8957.

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