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 $128,000 at 7.4%, compounded monthly. They make their regular monthly payments for 5 years, then decide to pay $1400 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 $1400. (Round your answer to the nearest cent.)
$  

(c) How many payments of $1400 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)

Their regular monthly payment is found using the following equation

Regular monthly payment = $ 886.25

------------------------------------------------------------------------------------------------

b)

The unpaid balance at the end of 5 years is found as follows

Unpaid balance = $ 120989.14

---------------------------------------------------------------------------------------------------

c)

By paying $ 1400 per month, the number of payments required to payoff the loan is found as follows

Solving for the value of t in the above equation,

-12 t ln 1.006166667 = ln 0.467071646

t = 123.83 months

It will take 123.83 monthly payments to payoff the loan.

----------------------------------------------------------------------

d)

Intererst according to old payment = $ 886.25 360 months - $ 128000 = $ 191050

The interest paid during the first 5 years is calculated as follows

Interest paid for the remaining months = $ 1400 123.83 months - $ 120989.14 ( unpaid balance at end of 5 years)

Interest paid for the remaining months = $ 52,372.86

Total interest paid = $ 52,372.86 + $ 57099.61 = $ 109,472.47

Interest saved = $ 191050 - $ 109,472.47

Interest saved = $ 81,577.53

By paying off the loan this way, the interest saved = $ 81,577.53