Question

Langara Woodcraft borrowed money to purchase equipment. The loan is repaid by making payments of ​$1058.69 at the end of every six months over five years. If interest is ​6.6% compounded annually​, what was the original loan​ balance?

Answer 1

The original loan balance was approximately $10,000.52.

Step-by-step explanation:

To find the original loan balance, we can use the formula for the present value of an annuity:

Loan Balance = PMT × [(1 - (1 + r)^(-n)) / r]

Where PMT is the payment amount, r is the interest rate per compounding period, and n is the total number of compounding periods.

In this case, the payment amount is $1058.69, the interest rate is 6.6% compounded annually (or 0.066), and the total number of compounding periods is 10 (5 years with semi-annual payments).

Plugging these values into the formula, we get:

Loan Balance = $1058.69 × [(1 - (1 + 0.066)^(-10)) / 0.066] ≈ $10,000.52

Therefore, the original loan balance was approximately $10,000.52.