Question

What would be the sum of all the payments made (i.e., total $s paid over the 30 years, ignoring time value) on the following house mortgage? Loan amount is $171,000 with an interest rate of 7.2% per annum, term of 30 years, and monthly payments. (Round to nearest penny and enter, for example, as 123456.78)

Answer 1

First, let us find the monthly payment, then we can multiply the monthly payment with the total number of payments to get the total amount paid.

To find monthly payment we can use the present value of annuity formula:

Where,
PVA = Present value of the annuity (this will be loan amount)
A = Annuity or monthly payment
i = Interest rate in decimal form
a = Number of payments in a year
n = Number of years

Therefore,

Total number of payments = 30 * 12 = 360 payments

Therefore,

The total amount paid = Monthly payment * Total number of payments

= $1,160.7278 * 360 .....................(note: here I have not rounded off the monthly payment)

=  $417,862.02

Therefore the total amount paid on the loan is $417,862.02.

.

If you want to do this on Excel refer the following:

Loan amount	$171,000
Interest rate	7.20%
Term in years	30
Number of payments in a year	12
Monthly payment	$1,160.73
Total amount paid	$417,862.02

Excel formulas: