Question

(Mortgage Loans MC)

A home buyer is debating between two different mortgages for $167,800. The options are:

Option A: 20-year fixed rate loan at 7.45% with a total of $323,198.36 paid in principal and interest over the life of the loan

Option B: 15-year fixed rate loan at the same rate.

How much more total principal and interest will the buyer pay for the 20-year loan versus the 15-year loan?

A spreadsheet was used to calculate the correct answer. Your answer may vary slightly depending on the technology used

$46,041.05
$44,061.05
$229,893.95
$292,893.95

Answer 1

Okay so:
Total payment = Loan amount x (rate/12) x (1 + rate/12)^n/1 + rate/12)^n -1
Loan amount = $167,800
Rate = 7.45% per year (or 0.0745 as a decimal)
Number of payments (n) = 15 years * 12 months/year = 180

Answer 2

The total amount paid in principal and interest for the 20-year loan is given as
$323,198.36.
To find out how much the buyer will pay in total for the 15-year loan, we first need to
calculate the monthly payment for the 15-year loan. The formula for the monthly pay-
ment of a loan is:
M = P[r(1 + r)"]/[(1 + r)” − 1]
-
where:
M is the monthly payment,
P is the principal loan amount,
r is the monthly interest rate (annual rate divided by 12),
n is the number of payments (months).
Substituting the given values into the formula:
r = 7.45/100/12 = 0.00620833
n = 15 * 12 = 180
P = $167,800
M = 167800[0.00620833(1+0.00620833)¹80]/[(1 +0.00620833)¹80 - 1]
After calculating the above expression, we find that the monthly payment for the 15-
year loan is approximately $1532.17.
The total amount paid over the life of the 15-year loan is then the monthly payment
times the number of payments:
Total = M * n = $1532.17 * 180 = $275,590.60
Finally, to find out how much more the buyer will pay for the 20-year loan versus the
15-year loan, subtract the total amount paid for the 15-year loan from the total amount
paid for the 20-year loan:
Difference = $323, 198.36 – $275, 590.60
So, the buyer will pay approximately $47, 607.76 more for the 20-year loan versus
the 15-year loan.

Answer 3

Next:
Total payment = $167,800 x (0.0745/12) x (1 + 0.0745/12)^180)/(1 + 0.0745)^180 -1

Answer 4

So based on the loan differences. (Which are)
Option A: Total paid = $323,198.36
Option B: approximately $269,157.31.
So, our correct answer would be $54,041.05 but our other closest option is $46,041.05 which is not exact.

Answer 5

thx man

Answer 6

No problemo

Answer 7

wait. it cant be 54,041.05

Answer 8

its not an answer choice and neither is yours D14610

Answer 9

Re-read the last part and look at the numbers silly

Answer 10

oh. but dont we have to get exact?

Answer 11

I said $46,041.05 would be the closest, which is one of the answers

Answer 12

yeah you did

Answer 13

It's the closest you have so.

Answer 14

ok. thx guys for answering