Final answer:
To find the present value of an ordinary annuity with $130 monthly payments for 12 years at 4% annual interest, compounded monthly, use the annuity present value formula incorporating the monthly payment amount, the monthly interest rate, and the total number of payments, and then round to the nearest cent.
Step-by-step explanation:
The question asks to calculate the present value of an ordinary annuity with monthly payments of $130 for 12 years at an annual interest rate of 4%, compounded monthly. To find the present value (PV), we use the formula for an ordinary annuity PV, which takes into account the periodic payment (R), the interest rate per period (i), and the total number of payments (n). Given that the interest is compounded monthly, the monthly interest rate is 4% divided by 12 months, which is 0.003333. The number of periods will be 12 years multiplied by 12 months, totaling 144 payments.
The formula for the present value of an ordinary annuity is:
PV = R × [(1 - (1 + i)^{-n}) / i]
In this case, R = $130, i = 0.003333, and n = 144. Plugging these values into the formula, we would perform the following calculation:
PV = $130 × [(1 - (1 + 0.003333)^{-144}) / 0.003333]
After performing the calculation, round the result to the nearest cent to get the present value of the annuity.