Question

Stumble Bum and his wife, Alex, just bought a new home and financed the purchase with $350,000 30-year fixed-rate loan at 4%. If they take 30 years to pay off the loan, what will be the lifetime interest they will pay? Note: solve with financial calculator.

A. $756,000

B. $601,500

C. $350,000

D. $251,543

Answer 1

So this needs to be solved step wise,

• Find the monthly payment
• Find the sum of all payments
• Find the difference between the loan amount and the sum of all payments. This is the total amount of interest

So in the financial calculator we input:

FV = 0, PV = 350000, I/Y = 4/12 = 0.33, N = 30 x 12 = 360

The we compute the PMT

PMT = -1670.95 This is a negative figure because we have to pay it and therefore it is an outflow. But we have to ignore the sign

If 1 payment = 1670.95 then the 360 payments will add up to 360 x 1670.95 =  $601,543

If the loan was 350000 and it took  $601,543 to pay it off then the interest on the same was  $601,543.27 -350000 =  $251,543.

So the correct option is D

We can solve it algebraically as follows:

We are given the following information:

r	4.00%
n	30
frequency	12
PV	$   3,50,000.00

We need to solve the following equation to arrive at the required PMT

Amortization schedule is as follows:

Opening balance = previous year's closing balance
Closing balance = Opening balance+Loan-Principal repayment
PMT is calculated as per the above formula
Interest = 0.04 /12 x opening balance
Principal repayment = PMT - Interest