Question

A borrower is making a choice between a mortgage with a monthly payments or biweekly payments. The loan will be $150,000 at 8% interest for 25 years. How much will he save if he uses biweekly payments?

Answer 1

Step 1
Calculation of monthly loan payment ($150000 loan @ 8% for 25 years)
We can use the present value of annuity formula to calculate the monthly loan payment.
Present value of annuity = P x {[1 - (1+r)^-n]/r}
Present value of annuity = loan amount = 150000
P = monthly loan payment = ?
r = interest rate per month = 8%/12 = 0.006667
n = number of months loan payment = 25 years x 12 = 300
150000 = P x {[1 - (1+0.006667)^-300]/0.006667}
150000 = P x 129.5645
P = 1157.72
Monthly loan payment = $1,157.72
Total payment if monthly option is selected = $1157.72 x 300 = $3,47,317.30
Step 2
Calculation of biweekly loan payment ($150000 loan @ 8% for 25 years)
We can use the present value of annuity formula to calculate the biweekly loan payment.
Present value of annuity = P x {[1 - (1+r)^-n]/r}
Present value of annuity = loan amount = 300000
P = bi weekly loan payment = ?
r = interest rate per two week = 8%/26 = 0.003077
n = number of bi weekly loan payment = 25 years x 26 = 650
150000 = P x {[1 - (1+0.003077)^-650]/0.003077}
150000 = P x 280.8808
P = 534.03
Bi weekly loan payment = $534.03
Total payment if bi weekly option is selected = $534.03 x 650 = $3,47,122.38
Step 3
A borrower will save $194.92 [$3,47,317.30 - $3,47,122.38] if he uses biweekly payments