Question

PLEASE ROUND TO THE NEAREST CENT FOR FINAL ANSWER

Compare the monthly payments and total loan costs for the following pairs of loan options. Assume that both loans are fixed rate and have the same closing costs.

You need a ​$130,000 loan.

Option​ 1: a​ 30-year loan at an APR of 9.5​%.

Option​ 2: a​ 15-year loan at an APR of 8.5%.

--------------------------------------------------------------------

1.) Find the monthly payment for each option.

The monthly payment for option 1 is what?

The monthly payment for option 2 is ​what?.

​(Do not round until the final answer. Then round to the nearest cent as​ needed.)

2.) Find the total payment for each option.

The total payment for option 1 is what?

The total payment for option 2 is what?

​(Round to the nearest cent as​ needed.)

Compare the two options. Which appears to be the better​ option?

A.Option 2 is the better​ option, but only if the borrower can afford the higher monthly payments over the entire term of the loan.

B.Option 1 will always be the better option.

C.Option 1 is the better​ option, but only if the borrower plans to stay in the same home for the entire term of the loan.

D.Option 2 will always be the better option

Answer 1

As we know that the formula for EMI is given by

EMI = [P x R x (1+R)^N]/[(1+R)^N -1]

Where

P = Principal or Loan Amount

R = Rate of interest (Monthly)

N = Total Monthly Payments

Now in question we have 2 options, we will solve for option 1

Option 1

P = 130000

R = 9.5/12 = 0.7916666667%

N = 12 months * 30 years = 360

Putting in the formula we get

EMI = [P x R x (1+R)^N]/[(1+R)^N -1]

= [130000 * (0.095/12) * (1+(0.095/12))^360]/(1+(0.095/12))^360 - 1)

= [130000 * (0.007916666667) * 17.0948617968]/16.0948617968

= 17,593.4619332808/16.0948617968

= 1,093.1104693784

= 1093.11

EMI = 1093.11

Total Payment for Option 1

So Total Payment = 1093.11 * 360

= 3,93,519.6

Option 2

P = 130000

R = 8.5/12 = 0.7083333333

N = 12 months * 15 years = 180

Putting in the formula we get

EMI = [P x R x (1+R)^N]/[(1+R)^N -1]

= [130000 * (0.085/12) * (1+(0.085/12))^180]/(1+(0.085/12))^180 -1)

= 3,280.6099462031/2.5626533352

= 1,280.1614253248

= 1280.16

EMI = 1280.16

So Total Payment = 1280.16 * 180

= 2,30,428.8

As the payment in option 2 is the best option as the total payment would be (393519.6 - 230428.8) = 1,63,091.6 less. The monthly payments would be higher by (1280.16/1093.11) - 1 = 17.11% higher so it might affect the payment capability of the borrower. So the Answer A

A. Option 2 is the better​ option, but only if the borrower can afford the higher monthly payments over the entire term of the loan.