Question

For 1≤n≤10 1 ≤ n ≤ 10 , find a formula for pn, the payment in year n on a loan of 105000 dollars. Interest is 3 percent per year, compounded annually, and payments are made at the end of each year for 10 years. Each payment is 10500 dollars plus the interest on the amount of money outstanding.

Answer 1

To find the payment in year n on a loan of $105,000 with an interest rate of 3%, use the formula for the future value of an annuity.

Step-by-step explanation:

To find the payment in year n on a loan of $105,000 with an interest rate of 3% compounded annually, we can use the formula for the future value of an annuity:

FV = P * ((1 + r)^n - 1) / r

Where FV is the future value, P is the payment amount, r is the interest rate, and n is the number of periods. In this case, n = 10 and FV = $105,000. Rearranging the formula, we can solve for P:

P = FV * r / ((1 + r)^n - 1)

Substituting the known values, we get:

P = $105,000 * 0.03 / ((1 + 0.03)^10 - 1) = $12,310

Therefore, the payment in year n on the loan will be $12,310.