Final answer:
To amortize a $7000 debt with an 11% interest rate compounded semiannually over 4 semiannual payments, one can use the present value of an annuity formula. By substituting the given values and solving for the payment size, it's determined that each payment should be approximately $1927.20.
Step-by-step explanation:
To determine the size of each semiannual payment needed to amortize a debt of $7000 with an interest rate of 11%, compounded semiannually, we use the present value of an annuity formula:
PV = R × [ (1 - (1 + i)⁻⁾) / i ]
Where:
- PV = present value of the annuity (the amount of the loan), which is $7000.
- R = the semiannual payment.
- i = the semiannual interest rate, which is 11% per year divided by 2, equating to 0.055.
- n = the total number of payments, which is 4.
Substituting the values into the formula and solving for R gives us:
$7000 = R × [ (1 - (1 + 0.055)⁻⁾) / 0.055 ]
Solving for R:
R = $7000 / × [ (1 - (1 + 0.055)⁻⁾) / 0.055 ]
After calculating, we find that the size of each semiannual payment rounded to the nearest cent is approximately $1927.20.