A debt of $6000 is to be amortized with 8 equal semiannual payments. If the interest rate is 5%, compounded semiannually, what is the size of each payment? (Round your answer to the nearest cent.)
1448.12
To find the size of each payment, we can use the formula for amortization of a loan:
Payment = Principal / Present Value Annuity Factor
In this case, the Principal is $6000 and there are 8 equal semiannual payments.
The Present Value Annuity Factor (PVAF) can be determined using the formula:
PVAF = (1 - (1 + r)^(-n)) / r
where r is the interest rate per period and n is the number of periods.
Since the interest rate is 5% compounded semiannually, the interest rate per period is 5% / 2 = 2.5%.
Substituting the values into the formula, we have:
PVAF = (1 - (1 + 0.025)^(-8)) / 0.025
Calculating this value gives a result of approximately 6.10149.
Now we can calculate the size of each payment:
Payment = Principal / PVAF
= $6000 / 6.10149
Calculating this value gives a result of approximately $982.55.
Therefore, the size of each payment, rounded to the nearest cent, is $982.55.