Question

. Which option is better for your purchase of a $230,000 home with a 18% down payment: A) Interest rate of 9.5% with a 15 year mortgage or B) Interest rate of 5.5% with a 30 year mortgage?
*****To answer which is "better" you must address which option has a lower monthly payment, *AND* which option will cost you more interest by the end of the loan. *****

Using the simple interest formula, for *both options above*, calculate the interest (I) you will be paying as a part of your FIRST monthly payment. (**Ask yourself: What is P? r? t? for the first month)

*For both options*: After calculating what your monthly payment would be AND what the interest of your first payment would be, figure out how much of that monthly payment is going to your principal. (**Ask yourself: What is the TOTAL monthly payment? How much of that is interest? So what is left?)
Show work

Answer 1

Option A:

Loan amount = Price of home * (1 - down payment)
= $230,000 * (1 - 0.18)
= $188,600.

PV = $188,600
Nper = 15 * 12 = 180
Rate = 9.5% / 12
FV =0

Monthly payment can be calculated by using the following excel formula:
=PMT(rate,nper,pv,fv)
=PMT(9.5%/12,180,-188600,0)
= $1,969.41

Monthly payment for option A = $1,969.41

Total payment = Monthly payment * number of months
= $1,969.41 * 180
= $354,493.40

Option B:

PV = $188,600
Nper = 30 * 12 = 360
Rate = 5.5% / 12
FV =0

Monthly payment can be calculated by using the following excel formula:
=PMT(rate,nper,pv,fv)
=PMT(5.5%/12,360,-188600,0)
= $1,070.85

Total payments = $1,070.85 * 360 = $385,506.02

Option B has lower monthly payment. But it will cost you more interest by the end of the loan. On the basis of the cost of interest, Option A is better.

Option A:

Interest on the first monthly payment = $188,600 * 9.5% * (1/12) = $1,493.08

Principal amount on first monthly payment = $1969.41 - $1493.08 = $476.32

Option B:

Interest on the first monthly payment = $188,600 * 5.5% * (1/12) = $864.42

Principal amount on first monthly payment = $1070.85 - $864.42 = $206.43