Final Answer:
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.