Answer to Question #210213 in Financial Math for tati

Question

A family has an $80,000, 20-year loan at 8% compounded monthly.

(a) Find the monthly payment and the total interest paid.

(b) Suppose the family decides to add an extra $100 to its mortgage payment each month starting with the very first payment. How long will it take the family to pay off the mortgage?

(c) Referring to part (i) and (ii), how much interest will the family save? 

Answer 1

(a) The monthly payments are the periodic and regular payments that are made by the borrowers for the loan that is taken by them and the interest is the amount of interest at a specified rate of interest that is paid to the lender by the borrower until the loan is paid in full.

The monthly payments are estimated with the help of the PMT function in excel using the present value of the loan, the rate of interest, and the time period, and the interest is estimated by deducting the present value of the loan from the total payments made for the loan.

Monthly Payments:

Therefore, the monthly payments made for the loan are $669.15.

Interest:

interest paid=monthly payments-present value$=(669.15\times20\times12)-80000=\$80596$

The total interest paid on the loan is $80,596. 

(b) Mortgage payments are the payments made for a mortgage loan and include the interest and principal payments for the mortgage loan. These payments are made for a time period until which the mortgage loan is fully paid by the borrower to the lender.

The time period or the number of years in which the borrowers will be able to pay off their mortgage loan if they pay additional payments by adding an extra mortgage payment to their regular payments will be estimated with the help of the Nper function on excel with the help of the monthly payments, rate, and present value.

Monthly Payments:

monthly payments =payments made+additional payment

$=669.15+100=\$769.15$

Time period:

Therefore, the loan can be repaid in 15 years or 178 months with additional payments. 

(c) - A loan is paid back by the borrower to the lender with additional payments of interest to the lender and the interest that is charged to the borrower is the finance charge that is charged to the borrower for using the borrowed amount and the interest is paid at a specified rate.

The interest that is saved by the borrower on the mortgage loan will be estimated with the help of the interest that is paid by the borrower when the payments were low and the interest that was paid with the additional payments. The difference between the two will be the interest saved.

Interest when higher payments are made:

interest with higher payments=total payments-loan

$=(178\times 769.15)-80000=\$ 56909$

Interest saved:

interest saved=lower payment interest-higher payment interest

$=80596-56909=\$ 23687$

Therefore, $23,687 of interest will be saved on the loan.