Question

An individual borrows $4,500 from the bank to be repaid in three equal annual installments, with the first installment to be paid one year after the loan amount is received. if interest on the loan is charged at a rate of 9 per cent per annum compounded annually, to the nearest dollar the annual installment is

a. $1,631
b. $1,778
c. $1,373
d. $1,259

Answer 1

To calculate the annual installment for a $4,500 loan at a 9% annual compounded interest rate, we use the annuity formula. After replacing the variables with our known values and solving, the final amount is rounded to the nearest dollar to provide the answer to the student.

Step-by-step explanation:

To determine the annual installment amount for repaying a loan of $4,500 with a 9% interest rate compounded annually over three years, we need to use the annuity formula. The annuity formula can be expressed as follows:

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

Where:

• PMT is the payment amount per period (which we are trying to calculate).
• P is the principal amount (the initial loan amount, which is $4,500).
• r is the interest rate per period (in decimal form; so 9% is 0.09).
• n is the number of periods (which in this case is 3, since the loan is to be repaid in three years).

We can place these numbers into our formula to calculate the yearly installment:

PMT = 4500 * (0.09(1+0.09)^3) / ((1+0.09)^3 - 1)

After calculating the above expression, we would round the result to the nearest dollar to find the closest answer.