Final answer:
To calculate the principal of the loan, use the present value formula. For this loan with payments of $4000.00 every six months for twelve years at 8% compounded quarterly, the principal is a. $75,655.69.
Step-by-step explanation:
To calculate the principal of the loan, we need to use the present value formula:
PV = PMT × ((1 - (1 + r/n)^(-n×t))/(r/n))
Where PV is the principal, PMT is the payment amount, r is the interest rate, n is the number of compounding periods per year, and t is the total number of years.
In this case, the payment amount is $4000.00, the interest rate is 8%, the compounding is quarterly (so n=4), and the total number of years is 12.
Substituting the values into the formula:
- PMT = $4000.00
- r = 8% = 0.08
- n = 4
- t = 12
PV = $4000.00 × ((1 - (1 + 0.08/4)^(-4×12))/(0.08/4)) = $75,655.69
Therefore, the principal of the loan is a. $75,655.69.