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