Question

Ricky is taking out a personal loan for $12,000 to remodel his kitchen.  He would like the lowest monthly payment possible, even if it means a bigger finance charge in the end.  His bank has offered him a loan at 13% interest for 36 months or 12% interest for 60 months, both of which are compounded monthly.  Which of the following statements most accurately describes what Ricky should be thinking?

Answer 1

To solve this we are going to use the monthly payment formula:
`P=(r(PV))/(1-(1+r)^(-n))`

where

`P` is the payment

`PV` is the amount of the loan

`r` is the rate per period

`n` is the number of periods

Option A. 13% interest for 36 months compounded monthly

We know form our problem that Ricky is taking out a personal loan for $12,000, so
`PV=12000`. We also know that the term of the loan is 36 months, so
`n=36`. To find the rate per period, we first need to convert the interest rate to decimal form; to do it, we divide the rate by 100%:
`(13)/(100) =0.13`. Now since the bank is charging him the interest rate for the 36 months, we just need to divide the interest rate (in decimal form) by the number of months (36) to find the rate per period:
`r=(0.13)/(36)`.

Now that we have all the vales we need, let's replace them in our formula

`P=(r(PV))/(1-(1+r)^(-n))`

`P=((0.13)/(36)(12000))/(1-(1+(0.13)/(36))^(-36))`

`P=356.07`

The monthly payment of loan A is $356.07

Option B 12% interest for 60 months compounded monthly

`PV=12000`

interest rate in decimal form =
`(12)/(100) =0.12`

`r=(0.12)/(60)`

Replace the values in formula:

`P=(r(PV))/(1-(1+r)^(-n))`

`P=((0.12)/(60)(12000))/(1-(1+(0.12)/(60))^(-60))`

`P=212.44`

The monthly payment of loan B is $212.44

Monthly payments of loan B are significantly low that monthly payments of loan A.

We can conclude that the correct answer is: a. More payments with the 60 month loan will give him the lowest monthly payment.