Question

A borrower takes out a 40 year, $140,000 loan. The loan has a 8.25% interest rate and is compounded 2 times a year. How much interest will be added to the loan over the term of the loan?

(Note: Round all results to 2 decimal places [i.e. ".05"])
(A = Pr(1+ i/n)nt- Pr
Where
-A = Amount of Interest
-Pr(1+ i/n)nt= Future Value
-Pr = Principal
-i = Annual Interest Rate
-n = Number of Times Compounded
-t = Number of Years in the Lifetime of the Loan
-(1+ i/n)nt = Compound Interest Factor)

Answer 1

To calculate the amount of interest added to the loan, use the formula A = Pr(1+ i/n)nt - Pr. Substitute the given values into the formula and calculate the expression.

Step-by-step explanation:

Compound interest is an interest rate calculation on the principal plus the accumulated interest.

To calculate the amount of interest added to the loan over the term, we can use the formula A = Pr(1+ i/n)nt - Pr, where:

• A is the amount of interest
• P is the principal (loan amount)
• r is the annual interest rate (8.25% expressed as decimal)
• n is the number of times the interest is compounded per year (2 times in this case)
• t is the number of years in the term of the loan (40 years)

Substituting the values into the formula, we have:

A = 140,000(1 + 0.0825/2)^(2*40) - 140,000

Calculating this expression will give us the amount of interest added to the loan over the term.