Respuesta :
Its D. the 36 month loan comes with a bigger finance charge in the en thus a bigger monthly pay
To solve this we are going to use the monthly payment formula: [tex] P=\frac{r(PV)}{1-(1+r)^{-n}} [/tex]
where
[tex] P [/tex] is the payment
[tex] PV [/tex] is the amount of the loan
[tex] r [/tex] is the rate per period
[tex] n [/tex] 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 [tex] PV=12000 [/tex]. We also know that the term of the loan is 36 months, so [tex] n=36 [/tex]. 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%: [tex] \frac{13}{100} =0.13 [/tex]. 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: [tex] r=\frac{0.13}{36} [/tex].
Now that we have all the vales we need, let's replace them in our formula
[tex] P=\frac{r(PV)}{1-(1+r)^{-n}} [/tex]
[tex] P=\frac{\frac{0.13}{36}(12000)}{1-(1+\frac{0.13}{36})^{-36}} [/tex]
[tex] P=356.07 [/tex]
The monthly payment of loan A is $356.07
Option B 12% interest for 60 months compounded monthly
[tex] PV=12000 [/tex]
interest rate in decimal form = [tex] \frac{12}{100} =0.12 [/tex]
[tex] r=\frac{0.12}{60} [/tex]
Replace the values in formula:
[tex] P=\frac{r(PV)}{1-(1+r)^{-n}} [/tex]
[tex] P=\frac{\frac{0.12}{60}(12000)}{1-(1+\frac{0.12}{60})^{-60}} [/tex]
[tex] P=212.44 [/tex]
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.
