Final answer:
To calculate the monthly payment R to accumulate $13,000 over 6 years with a 3.1% annual interest rate compounded monthly, we use the future value of an annuity formula and substitute the given values. After solving the equation, we round the result to the nearest cent.
Step-by-step explanation:
To find the monthly payment R needed to accumulate $13,000 with 72 monthly installments over 6 years at an annual interest rate of 3.1% compounded monthly, we use the formula for the future value of an annuity:
[FV = R times frac{{(1 + i)^n - 1}}{i}]
Where:
- FV is the future value, which is $13,000.
- R is the monthly payment.
- i is the monthly interest rate, which is 3.1% per year or 0.031/12 per month.
- n is the total number of payments, which is 6 years times 12 months/year = 72 payments.
We rearrange the formula to solve for R:
[R = frac{FV times i}{{(1 + i)^n - 1}}]
Substituting the given values:
[R = frac{13000 times frac{0.031}{12}}{{(1 + frac{0.031}{12})^{72} - 1}}]
After calculating using this formula, we would round the result to the nearest cent to find the monthly payment required.