Final answer:
To determine the semi-annual payment amount for a loan compounded semi-annually, one would use the present value of an annuity formula, considering the loan amount, interest rate per period, and total number of payments.
Step-by-step explanation:
To calculate the size of the periodic payment for a loan of $21,750.00 at 3.50% compounded semi-annually, which is to be repaid over 3 years with payments at the end of every 6 months, we would use the formula for the present value of an annuity. Given the nature of the question, we use the following formula where R represents the payment amount.
PV = R x [1 - (1 + i)^(-n)] / i
Where:
PV is the present value or loan amount which is $21,750.00
R is the periodic payment amount
i is the interest rate per period (semi-annual)
n is the total number of payments (3 years semi-annually is 6 payments)
We first need to calculate i, which is the semi-annual rate: i = 3.50% / 2 = 1.75% or 0.0175 in decimal. Next, we determine the value of n, which is the number of semi-annual periods in 3 years: n = 3 years x 2 = 6 periods.
Unfortunately, without further examples or actual calculations, we cannot compute the exact payment amount here. However, the method described is how one would determine the semi-annual payment amount.