Question

Create a program that calculate the amount of a mortgage payment. Refer to the appropriate video or any online source for how the mathematics of the calculation works. If given these three things:

• The amount of the loan in whole dollars
• The number of payments (e.g. 360 for 30-year)
• The interest rate per payment period in percent ( a positive floating-point number)

The program should print out the correct value (in dollars and cents) of the per-period payment of principal and interest (ignore escrow accounts, taxes, and insurance) for the following scenarios:

• 72 month loan of $20,000, 4.4% APR, compounded monthly
• 30 year loan of $150,000, 5% APR, one annual payment each year for 30 years

I am confused with the math behind finding the amount of a mortgage payment. Please explain the calculations behind the two above given scenarios.

Answer 1

1) Compute the monthly payment of loan of $20000 to be financed over 72 months at an interest rate of 4.4% compounded monthly

According to given information principal is $20000

Rate of interest r = 4.4%

Rate of interest r = 4.4 / 100 = 0.044

Compounding period is monthly so r = 0.044 / 12 = 0.003667

Now number of payments 72

Now we can use the below formula to find the monthly payment (PMT)

PMT = [ p x r x (1+r)^t ] / [(1+r)^t-1]

PMT = [20000 x 0.003667 x (1+0.003667)⁷² ] / [(1+0.003667)⁷²-1]

PMT = [73.34 x 1.30153] / [1.30153 - 1]

PMT = [95.4542] / [0.30153]

PMT = $316.57

So monthly payment is $ 316.57

2) Compute the monthly payment of loan of $150000 to be financed over 30 years at an interest rate of 5% for annual payments

According to given information principal is $150000

Rate of interest r = 5%

Rate of interest r = 5 / 100 = 0.05

Now number of payments 30

Now we can use the below formula to find the monthly payment (PMT)

PMT = [ p x r x (1+r)^t ] / [(1+r)^t-1]

PMT = [150000 x 0.05 x (1+0.05)³⁰ ] / [(1+0.05)³⁰-1]

PMT = [7500 x 4.3219] / [4.3219 - 1]

PMT = [32414.25] / [3.3219]

PMT = $9757.744 ~ 9757.75

So annual payment is $ 9757.75