Question

You take out a $250,000 30 year mortgage with monthly payments and a rate of 10%, monthly compounded. What will your mortgage balance be after your first year of making your monthly payments? How much total interest you paid on this mortgage?

work out on a financial calculator. explain the steps to take please.

Answer 1

Monthly payment (PMT) on loan can be calculated with the help of PV of an Annuity formula

PV = PMT * [1-(1+i) ^-n)]/i

Where,

Present value (PV) of loan =$250,000

PMT = Monthly payment =?

n = N = number of payments = 12 *30 years = 360 payments

i =monthly interest rate = 10%/12 = 0.833% per month

Therefore,

$250,000 = PMT* [1- (1+0.833%) ^-360]/0.833%

= $2,193.93

Again we can use same formula to calculate mortgage balance after your first year of making your monthly payments in following manner-

PV = PMT * [1-(1+i) ^-n)]/i

Where PV of loan (unpaid balance at the end of first year) =?

PMT = Monthly payment = $2,193.93

n = N = number of remaining payments = 360 -12 = 348 month    [one year has 12 months]

i = I/Y = monthly interest rate = annual interest rate/ 12 = 10%/12 =0.833% per month

Therefore,

PV = $2,193.93* [1- (1+0.833%)^-348]/0.833%

PV = $248,610.30

Therefore mortgage balance after your first year of making your monthly payments is $248,610.30

Total interest paid over the life of the loan = Number of payments * Monthly payment – Initial Loan amount

= 360 * $2,193.93 - $250,000

= $789,814.41 - $250,000

= $539,814.41