Final answer:
To calculate the annual payment for a $2,400 loan with a 10% interest rate repaid over four years, one must use the annuity formula, accounting for present value, interest rate, and number of payments. The annual payment can be computed using a financial calculator or via iteration if done by hand.
Step-by-step explanation:
When borrowing $2,400 with an agreement to repay the loan in four equal annual payments at an interest rate of 10%, the calculation of your payment involves an annuity formula. The annuity formula considers the present value of a series of equal payments to be made in the future, taking into account interest accrued over the loan's term. To solve for the annual payment, we set up the equation based on the formula for the present value of an annuity:
PV = PMT × × × × × × × × × × × × × × × × (× × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × 1 - (1 + r)^-n)/r
In this formula, PV represents the present value ($2,400), PMT is the annual payment we are solving for, r is the annual interest rate expressed as a decimal (0.10 for 10%), and n is the number of payments (4 in this case).
After rearranging the formula to solve for PMT and substituting the values, we can calculate the annual payment amount. This requires either the use of a financial calculator or solving it through an iterative process if done by hand since the equation involves an exponent.
Understanding these calculations is important as it affects the total amount paid over the life of the loan, since interest can accumulate significantly, sometimes resulting in a total repayment more than double the original borrowed amount.