Question

A druggist borrows $3000 from a bank to stock her drugstore. The interest rate is 6% compounded semiannually with payments due every 6 months. She wants to repay the loan in 18 months. How much are the semiannual payments? (Round your final answer to two decimal places.)

Answer 1

To calculate the semiannual payments, use the formula for the present value of an annuity. In this case, the semiannual payments would be $1025.98.

Step-by-step explanation:

To calculate the semiannual payments, we can use the formula for the present value of an annuity:

PV = R * (1 - (1+i)^(-n)) / i

Where:
R = semiannual payment
i = interest rate per period
n = total number of periods

In this case, the loan amount is $3000, the interest rate is 6% compounded semiannually, and the loan duration is 18 months, which is equivalent to 3 periods. The interest rate per period would be 6% / 2 = 3%.

Substituting the values into the formula:

PV = $3000 = R * (1 - (1+0.03)^(-3)) / 0.03

Solving for R:

R = $3000 * 0.03 / (1 - (1+0.03)^(-3))

Rounding the final answer to two decimal places:

R = $1025.98