Question

What payment is required at the end of each year for 5 years to repay a loan of $3,310.00 at 11% compounded annually? The payment is $ (Round the final answer to the nearest cent as needed. Round all intermediate values to six decimal places as needed.)

Answer 1

The payment required at the end of each year for 5 years to repay a loan of $3,310.00 at 11% compounded annually is approximately $845.03.

Step-by-step explanation:

To calculate the annual payment, we can use the formula for the future value of an ordinary annuity. The formula is given by:

`\[ PMT = P * \left( (r(1+r)^n)/((1+r)^n - 1) \right) \]`

where:

- \(PMT\) is the payment,

- \(P\) is the principal amount (loan amount),

- \(r\) is the annual interest rate, and

- \(n\) is the number of compounding periods.

In this case, \(P = $3,310.00\), \(r = 11\% = 0.11\), and \(n = 5\) years. Plugging in these values, we get:

`\[ PMT = 3310 * \left( (0.11(1+0.11)^5)/((1+0.11)^5 - 1) \right) \]`

After evaluating this expression, we find that the annual payment is approximately $845.03. This means that in order to fully repay the loan over 5 years with an 11% annual interest rate, an annual payment of $845.03 is required.

It's essential to use this formula to ensure the correct calculation of periodic payments in loans, mortgages, or investments where compounding interest plays a significant role