Final answer:
The size of the monthly payments at an 8.1% interest rate compounded monthly for a contract valued at $11,900, stretched over 6 years, can be found using the present value of an annuity formula. By rearranging the formula to solve for R, the monthly payment, and substituting the known values into the equation, one can calculate the precise monthly payment required.
Step-by-step explanation:
The question pertains to calculating the size of monthly payments for an installment payment plan using the present value of an annuity formula, considering a given interest rate that is compounded monthly. The formula required for this calculation is:
PV = R * [(1 - (1 + i)^(-n))/i]
Where:
- PV is the present value of the annuity (the amount of the contract), which is $11,900.
- R is the monthly payment.
- i is the monthly interest rate, which is the annual rate divided by 12.
- n is the total number of payments (72, since it's 6 years multiplied by 12 months per year).
To find R, the formula is rearranged to:
R = PV / [(1 - (1 + i)^(-n))/i]
Using the given information:
R = $11,900 / [(1 - (1 + 0.081/12)^(-72))/(0.081/12)]
After computing the above equation, the result will be the monthly payment required to satisfy the contract under the given terms.