Question

What is the present value of an ordinary annuity with 10 payments of $9,400 if the appropriate interest rate is 5.5%?

Answer 1

The present value of an ordinary annuity with 10 payments of $9,400 at an interest rate of 5.5% is approximately $80,768.14.

Step-by-step explanation:

The present value of an ordinary annuity is calculated using the formula
`PV = PMT * [(1 - (1 + r)^(-n)) / r]`, where PV is the present value, PMT is the periodic payment, r is the interest rate per period, and n is the number of periods. In this scenario, the periodic payment (PMT) is $9,400, the interest rate (r) is 5.5%, and the number of periods (n) is 10.

Plugging these values into the formula, we get
`PV = $9,400 * [(1 - (1 + 0.055)^(-10)) / 0.055].` By solving this expression, the present value is found to be approximately $80,768.14. This means that the sum of the future cash flows, discounted at a rate of 5.5%, is equivalent to $80,768.14 in present value terms.

Understanding the present value of an annuity is crucial for financial decision-making, as it helps assess the current worth of a series of future cash flows. In this case, it indicates the amount that, if invested today at a 5.5% interest rate, would yield the same total value as the series of $9,400 payments over 10 periods.