Final answer:
The present value of an ordinary annuity with annual payments of $70,000 for 15 years at a 4% annual interest rate is approximately $778,288.00.
Step-by-step explanation:
To find the present value of an ordinary annuity with payments of $70,000.00 paid annually for 15 years at an interest rate of 4% per year compounded annually, you utilize the present value formula for an ordinary annuity. The formula is as follows:
Present Value of Annuity (PVA) = Pmt * [(1 - (1 + r)^-n) / r]
Where:
- Pmt is the annual payment amount
- r is the annual interest rate (in decimal form)
- n is the total number of payments
For this question:
- Pmt = $70,000
- r = 0.04 (4% as a decimal)
- n = 15
Substituting our values into the formula gives us:
PVA = $70,000 * [(1 - (1 + 0.04)^-15) / 0.04]
After calculating:
PVA = $70,000 * [(1 - (1 + 0.04)^-15) / 0.04]
PVA ≈ $70,000 * 11.1184
PVA ≈ $778,288
Therefore, the present value of the annuity is approximately $778,288.00. Remember to round your final answer to the nearest cent, which in this case does not change the value since there are no fractional cents.