Question

For mortgage loan of $140, 000 at an interest rate of 10. 5% per year for 25 years,
determine the
a) monthly mortgage payment,
b) total payments,
c) total interest over the period of 25 years.

Answer 1

Given :

Principle amount : $140000

Rate of interest : 10.5%

Time : 25 years

To find :

• The monthly mortgage payment
• Total payments
• Total interest over the period of 25 years.

Solution :

To find the monthly payments of the mortgage, first we should find the simple interest and total amount/total payments.

Simple interest :

${\sf \dashrightarrow \dfrac{P \times R \times T}{100}}$

${\sf \dashrightarrow \dfrac{140000 \times 10.5 \times 25}{100}}$

${\sf \dashrightarrow \dfrac{140000 \times 262.5}{100}}$

${\sf \dashrightarrow \dfrac{1400 \times 262.5}{1} = \dfrac{367500}{1}}$

${\sf \dashrightarrow \cancel \dfrac{367500}{1} = 367500}$

Hence, the interest received over the period of 25 years is ₹367500.

Now, let's find the total amount to be paid at end of the time period.

Total payments :

${\sf \dashrightarrow Simple \: interest + Principle}$

${\sf \dashrightarrow 367500 + 140000}$

${\sf \dashrightarrow 507500}$

Hence, the total payments done after the time period is ₹507500.

Now, we can find the monthly mortgage payments of this loan.

Monthly mortgage payments :

${\sf \dashrightarrow 507500 \div (25 \times 12)}$

${\sf \dashrightarrow \dfrac{507500}{300} = \dfrac{5075}{3}}$

${\sf \dashrightarrow \cancel \dfrac{5075}{3} = 1691.66}$

Hence, the monthly mortgage payments of the loan is ₹1691.66.