Question

Miles and Nick each separately apply for and receive loans worth $5,000 apiece. Miles has a very good credit score, so his loan has an APR of 7.75%, compounded monthly. Nick’s credit score is rather low, so his loan has an APR of 13.10% interest, compounded monthly. If both of them repay their loans over a four year period, making equal monthly payments based on their own loan, how much more will Nick have paid than Miles? (Round all dollar values to the nearest cent.) a.$619.68 b.$267.50 c.$1,609.57 d.$1,070.00

Answer 1

Answer:

Ans. Nick paid $619.68 more than Miles (exactly $619.54). So the answer is A)

Step-by-step explanation:

Hi, first we need to find the equal monthly payments for both, Miles and Nick, for that, we need to find the effective monthly rate (because the payments are going to be made monthly), also, we need to convert that 4 year period into months. After doing all that, we need to use the following equation and solve for "A".

$Present Value=\frac{A((1+r)^{n} -1)}{r(1+r)^{n} }$

Where:

A= monthly payments

r= rate of interest (for Miles is 0.075/12=0.006458 and Nick 0.131/12=0.010916)

n= number of periodic payments (both are 4*12=48 months)

First, let´s find out how much money Miles has to pay every month.

$5,000=\frac{A((1+0.00645833)^{48} -1)}{0.00645833(1+0.00645833)^{48} }$

$5,000=A(41.1594758)$

$A=121.48$

So, Miles has to pay $121.48 every month, for 48 months, that is a total of $5,830.98 (121.48*48=5,830.98)

Now, let´s do Nick

$5,000=\frac{A((1+0.01091667)^{48} -1)}{0.01091667(1+0.01091667)^{48} }$

$5,000=A(37.2063189)$

$A=134.39$

So, Nick has to pay $134.39 every month, for 48 months, that is a total of $6,450.52 (134.39*48=6,450.52)

The difference is 6,450.52- 5,830.98=619.54

Means that Nick has to pay $619.54 more than Miles. To your answers, the closest is A) $619.68.

Best of luck

Answer 2

Miles: 7.75% (0.0775) x 5,000 = $387.5 x 4 = $1550 (over four year period) Nick: 13.10% (0.131) x 5,000 = $655 x 4 = $2620 $2620 - $1550 = $1,070 (rounded to nearest cent) So the answer is D.