Question

6. You are saving up to buy a car. If you deposit $125 a month, every month, into a savings account earning 3% interest, compounded monthly, what is the balance after 2 years?

Answer 1

Solution:

The formula for calculating the Future value of savings at the end of “t” years with “ n” compounding periods in a year is

FV = P * [ [ ( 1 + ( r/n ) ) ( n * t) - 1 ] / ( r/ n) ]

Where FV = Future Value ; P = Periodic Deposit ;   r = rate of interest   ; t = time in years   ;

n = No. of compounding periods in a year

A per the information given in the question we have

P = $ 125 ; r = 3 % = 0.03 ; t = 2 years   ; n = 12 ; ( since compounding is monthly )

To find FV = Future Value ;  

Applying the above values in the formula we have:

= $ 125 * [ [ ( 1 + ( 0.03 / 12 ) ) ( 12 * 2 )   - 1 ] / ( 0.03 / 12 ) ]         

= $ 125 * [ [ ( 1 + 0.0025 ) (12 * 2)   - 1 ] / 0.0025 ]

= $ 125 * [ [ ( 1.0025 ) 24   - 1 ] / 0.0025 ]

= $ 125 * [ [ 1.061757 - 1 ] / 0.0025 ]

= $ 125 * [ 0.061757 / 0.0025 ]

= $ 125 * 24.702818

= $ 3,087.852213

= $ 3,087.8522 ( when rounded off to four decimal places )

= $ 3,087.85 ( when rounded off to two decimal places )

Thus the balance after two years = $ 3,087.85

Note: The value of ( 1.0025 ) 24   is calculated using the Excel formula =POWER(Number,Power)

=POWER(1.0025,24) = 1.061757