In: Accounting
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 ) ) ( t * n ) - 1 ] / ( r/ n) ]
Where
FV = Future Value ; P = Periodic Deposit i.e., r = Annual 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 = $ 390 ; r = 3 % = 0.03 ; t = 10 months = ( 10 / 12 ) = 0.833333 years ;
n = 12 ( since compounding is monthly ) ; To find FV = Future value ;
Applying the above values in the formula we have:
= $ 390 * [ [ ( 1 + ( 0.03 / 12 ) ) ( 0.833333 * 12 ) - 1 ] / ( 0.03 / 12 ) ]
= $ 390 * [ [ ( 1 + ( 0.03 / 12 ) ) ( 10 ) - 1 ] / ( 0.03 / 12 ) ]
= $ 390 * [ [ ( 1 + 0.0025 ) 10 - 1 ] / 0.0025 ]
= $ 390 * [ [ ( 1.0025 ) 10 - 1 ] / 0.0025]
= $ 390 * [ [ 1.025283 - 1 ] / 0.0025 ]
= $ 390 * [ 0.025283 / 0.0025 ]
= $ 390 * 10.113253
= $ 3,944.168784
FV = $ 3,944.17 ( when rounded off to the nearest cent )
Thus the savings plan balance after 10 months = $ 3,944.17
Note: The value of ( 1.0025 ) 10 is calculated using the Excel function =POWER(Number,Power)
=POWER(1.0025,10) = 1.025283