Question

Fritz Benjamin buys a car costing $8700. He agrees to make payments at the end of each monthly period for 8 years. He pays 10.8% interest, compounded monthly. What is the amount of each payment? Find the total amount of interest Fritz will pay.

Answer 1

Solution :

Calculation of each monthly payment :

The formula for calculating the monthly payment is

P = ( r * I ) / [ 1 – ( 1 / ( 1 + r ) n ) ]

Where

r = rate of interest   ; I = Amount of investment   ; n = No. of compounding periods

As per the information given in the question we have

r = 10.8 % / 12 = 0.9 % = 0.009 ( since the compounding is monthly )

I = Amount of investment = Cost of car = $ 8,700

n = No. of compounding periods = 8 years * 12 months = 96 months

Applying the above information in the formula we have monthly payment as

= ( 0.009 * $ 8,700 ) / [ 1 – ( 1 / ( 1 + 0.009 ) 96 ) ]

= $ 78.30 / [ 1 – ( 1 / ( 1.009 ) 96 ) ]

= $ 78.30 / [ 1 – ( 1 / 2.363480 ) ]

= $ 78.30 / [ 1 – 0.423105 ]

= $ 78.30 / 0.576895

= $ 135.726579

= $ 135.7266 ( when rounded off to four decimal places )

= $ 135.73 ( when rounded off to two decimal places )

Thus the monthly Payment = $ 135.73

Note : ( 1.009 ) ( 96 ) = 2.363480 is calculated using the excel formula =POWER(Number,Power)

=POWER(1.009,96)

Calculation of Total amount of Interest :

The total amount of Interest can be calculated as follows

= ( Amount of each Monthly payment * No. of monthly Payments ) – Cost of the car

As per the information available we have

Amount of each Monthly payment = $ 135.726579   ; No. of monthly Payments = 96   ;

Cost of the car = $ 8,700

Applying the above information in the formula we have

= ( $ 135.726579 * 96 ) - $ 8,700

= $ 13,029.751555 - $ 8,700

= $ 4,329.751555

= $ 4,329.7516 ( when rounded off to four decimal places )

= $ 4,329.75 ( when rounded off to two decimal places )

Thus the total amount of Interest that Fritz will pay = $ 4,329.75