Question

find the savings plan balance after 10 months with an apr of 3% and monthly payments of $390

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 ) ) ^{( 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