Question

If you borrow $2,400 and agree to repay the loan in four equal annual payments at an interest rate of 10%, what will your payment be? note: do not round intermediate calculations. round your answer to 2 decimal places. what will your payment be if you make the first payment on the loan immediately instead of at the end of the first year? note: do not round intermediate calculations. round your answer to 2 decimal places.

Answer 1

Your annual payment, if you borrow $2,400 with a 10% interest rate and agree to repay the loan in four equal annual payments, is $792.89. If you choose to make the first payment immediately instead of at the end of the first year, your immediate payment will be $764.35.

Step-by-step explanation:

In order to determine the annual payment for the loan, we can use the formula for the present value of an annuity, which is given by:

PV =C× (1 - (1 + r)^{-n}/r

where (PV) is the present value of the annuity, (C) is the annual payment, r is the interest rate per period, and (n) is the number of periods.

Given that you borrow $2,400 with a 10% interest rate and agree to repay the loan in four equal annual payments, we substitute the values into the formula:

2400 = C × (1 - (1 + 0.10)^{-4}/0.10}]

Solving for (C), we find that the annual payment (C) is $792.89.

Now, if you choose to make the first payment immediately, it effectively reduces the number of compounding periods to three. Adjusting the formula accordingly:

2400 = C × (1 - (1 + 0.10)^{-3})/{0.10}

Solving for (C) in this case gives an immediate payment (C) of $764.35. Therefore, making the first payment immediately reduces the annual payment amount.