Question

Purchase of a new home

The Does have qualified for a mortgage of $500,000 to be amortized over 25 years. Their mortgage broker has offered them the following options:

a. A 5 year fixed rate with monthly payments at an annual interest rate of prime+1%

b. A 10 year fixed rate with biweekly payments at an annual interest rate of prime+2%

Prime is currently at 1.5% and projected to increase by 0.25% every year for the next 10 years.

Which Mortgage terms should they accept given that their goal is to pay as much principle as possible over the next 10 years?

Answer 1

Answers:

a)

Interest rate forms an AP series starting from year 1 to year 25

2.5,2.75,...........8.5. Sum of anAPseres=25/2∗(2.5+8.5)=275/2

Therefore we take the average of the interest rates 275/(2∗25)=5.5

.

So using a financial calculator,

PV=−500000N=25∗12I/Y=5.5/12FV=0 , so we get PMT=3070.4

b)

Interest rate forms an AP series starting from year 1 to year 25

3.5,3.75,...........9.5 Sum of an AP series =25/2∗(3.5+9.5)=325/2

Therefore we take the average of the interest rates 325/(2∗25)=6.5

So using a financial calculator,

PV=−500000N=25∗26I/Y=6.5/26FV=0 , so we get PMT=1557

Therefore, they should accept the first mortgage plan.