What is the total amount owing on a $300,000 mortgage after 5 years at 7.75% compounded monthly?

To determine the total amount owing on a $300,000 mortgage after 5 years at an interest rate of 7.75% compounded monthly, it's important to use the formula for compound interest. The formula for calculating the future value of a loan or investment with compound interest is:

[ A = P \left(1 + \frac{r}{n}\right)^{nt} ]

Where:

• ( A ) is the amount of money accumulated after n years, including interest.

• ( P ) is the principal amount (the initial amount of money).

• ( r ) is the annual interest rate (decimal).

• ( n ) is the number of times interest is compounded per year.

• ( t ) is the number of years the money is borrowed or invested.

In the case of the mortgage:

• The principal ( P = 300,000 ).

• The annual interest rate ( r = 0.0775 ) (7.75% expressed as a decimal).

• Interest is compounded monthly, so ( n = 12 ).

• The time period ( t = 5 ) years.

Substituting these values into the formula gives:

[

A = 300,