Final answer:
To find the monthly payments for a contract of $12,200 at a 7.4% interest rate compounded monthly over 8 years, utilize the present value formula for an annuity and rearrange it to solve for the monthly payment (PMT). The necessary elements for the computation are the present value (PV), the monthly interest rate (r), and the total number of monthly payments (n).
Step-by-step explanation:
The question involves calculating the size of monthly payments needed to satisfy a contract with a present value of $12,200 at an interest rate of 7.4% compounded monthly over 8 years. Understanding the concept requires knowledge of present value of an annuity and annuity payment formulas.
Calculating the Monthly Payment
To calculate monthly payments, we need to use the formula for the present value of an annuity:
PV = PMT × ((1 - (1 + r)^(-n)) / r)
Where:
- PV is the present value or total amount of the contract. In this case, $12,200.
- PMT is the monthly payment.
- r is the monthly interest rate expressed as a decimal, which is 7.4%/12 months = 0.0074.
- n is the total number of payments, which is 8 years × 12 months/year = 96 months.
Plugging in the values into the formula and solving for PMT will give us the monthly payment amount.
Solving for Monthly Payment
To solve for PMT, you rearrange the formula:
PMT = PV / ((1 - (1 + r)^(-n)) / r)
After completing the calculations, we would arrive at the exact monthly payment required to pay off the contract over 8 years at a 7.4% interest rate.