Question

Your are comparing two options for a home mortgage. The first option is a 15-year mortgage with a 3.75% annual rate, and the second option is a 30-year mortgage with a 4% interest rate for a 500,000 loan. If you want your monthly payment under the first option to be the same as the monthly payment under the 30-year option, how much additional down payment will you neet to put dow under the 15-year option?

Answer 1

The answer is $171,754.46

Calculations:

Let the down payment in case of 1st option be "x". Thus loan amount = 500,000-x

Monthly payment will be computed using the "PMT" function in excel. Duration = 15 years *12 months = 180 months

Thus monthly payment in case of 1st option = PMT(3.75%/12, 180, 500000-x)

2nd option: Here duration = 30*12 = 360, rate is 4%. Let the down payment be y. Thus loan amount is 500,000 - y

Monthly payment here is PMT (4%/12, 360, 500000-y)

As monthly payments are same under both situations we can say that PMT(3.75%/12, 180, 500000-x) = PMT (4%/12, 360, 500000-y)

Solving the above using the "solver" function in excel we get x = $171,754.46 and y = $0. Monthly payments will be $2,387.08 in both cases.

Thus additional down-payment to be made = x- y

= $171,754.46 - 0

= $171,754.46

Option 1
x	171,754.29
Loan	328,245.71
duration	180.00
Monthly payment	-2,387.08

Option 2
y	0.00
Loan	500,000.00
duration	360.00
Monthly payment	-2,387.08