Question

This problem is a complex financial problem that requires several skills, perhaps some from previous sections.

Clark and Lana take a 30-year home mortgage of $129,000 at 7.2%, compounded monthly. They make their regular monthly payments for 5 years, then decide to pay $1500 per month.

(a) Find their regular monthly payment. (Round your answer to the nearest cent.)
$  

(b) Find the unpaid balance when they begin paying the $1500. (Round your answer to the nearest cent.)
$  

(c) How many payments of $1500 will it take to pay off the loan? Give the answer correct to two decimal places.
monthly payments

(d) Use your answer to part (c) to find how much interest they save by paying the loan this way. (Round your answer to the nearest cent.)

$

Answer 1

a) PV of Loan = 129,000
Rate per month = 7.2%/12 = 0.6%
Number of Periods = 30*12 = 360
Periodic Monthly payment for 5 years = PV/(1-(1+r)^-n)/r = 129,000/(1-(1+0.6%)^-360/0.6% =875.63679 or 875.64

b) The unpaid Balance at year 5 = PV*(1+r)ⁿ - PMT*((1+r)ⁿ-1)/r = 129,000*(1+0.6%)⁶⁰ - 875.63679*((1+0.6%)⁶⁰ - 1)/0.6% =
121,685.74

c) PV at year 5 = 1500*(1-(1+r)^-n)/r
121,685.74 = 1500*(1-(1+0.6%)^-n)/0.6%
121,685.74*0.6%/1500 = 1-1.006^-n
1.006^-n = 1 - 121,685.74*0.6%/1500
1.006^-n = 1- 0.486743
1.006^-n = 0.513257
applying log on both sides
-n log 1.006 = log(0.5132570
n = - log(0.5132570)/log1.006 = 111.49 months or 9.29 years

d) Interest Savings = FV of 1500 at 111.492 months - FV of 875.63679 at 111.492 = 1500*((1+0.6%)^111.492-1)/0.6% -875.63679*((1+0.6%)^111.492-1)/0.6% = 98,684.92

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