Calculate the monthly payment of a 30-year mortgage that is equal to $260,000 an
ID: 2790316 • Letter: C
Question
Calculate the monthly payment of a 30-year mortgage that is equal to $260,000 and the annual percentage rate equal to 6.5% (Show all calculator inputs and related calculations)
Calculate the total interest you will pay over the life of this loan. (Show all calculator inputs and related calculations)
a) in how many years you would have repaid the loan (Show all calculator inputs and related calculations)
b) how much less interest you would have paid than the interest amount of the original loan if you made that extra $100 payment each month. (Show all calculator inputs and related calculations)
Explanation / Answer
Answer 1.
Loan Balance = $260,000
Annual Interest Rate = 6.5%
Monthly Interest Rate = 6.50%/12 = 0.5417%
Period of loan = 30 years or 360 months
Monthly Payment = $260,000 / PVA of $1 (0.5417%, 360)
PVA of $1 (0.5417%, 360) = (1 - (1 / 1.005417)^360) / 0.005417
PVA of $1 (0.5417%, 360) = 158.20424
Monthly Payment = $260,000 / 158.20424
Monthly Payment = $1,643.45
Using financial calculator:
PV = 260,000
I/Y = 6.5%
C/Y = 12
N = 360
PMT = 1643.45
So, monthly payment is $1,643.45
Answer 2.
Total Amount paid = $1,643.45 * 360
Total Amount paid = $591,642
Amount borrowed = $260,000
Total Interest Paid = $591,642 - $260,000
Total Interest Paid = $331,642
Answer a.
If extra $100 per month is paid:
Monthly Payment = $1,643.45 + $100
Monthly Payment = $1,743.45
Monthly Interest rate = 0.5417%
Loan amount = $260,000
Using financial calculator:
PV = 260,000
I/Y = 6.50%
C/Y = 12
PMT = 1743.45
N = 305
Loan will be repaid in 305 months
Answer b.
Total Amount paid = $1,743.45 * 305
Total Amount paid = $531,752.25
Amount borrowed = $260,000
Total Interest Paid = $531,752.25 - $260,000
Total Interest Paid = $271,752.25
So, we will save interest of $59,889.75 ($331,642 - $271,752.25)
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