Question

You are considering investing in an ordinary annuity that will pay you $1,000 per year for 10 years. The interest rate is 5% per year. What is the present value of the annuity?

Answer 1

The present value of the annuity, considering an interest rate of 5% per year and $1,000 payments for 10 years, can be calculated using the present value of an ordinary annuity formula. The present value is approximately $8,513.63.

Step-by-step explanation:

To calculate the present value of an ordinary annuity, the formula PVA = PMT x [(1 - (1 + r)^(-n)) / r] is used, where PVA is the present value of the annuity, PMT is the annual payment, r is the interest rate per period, and n is the total number of periods. In this scenario, the annual payment (PMT) is $1,000, the interest rate (r) is 5% or 0.05, and the number of periods (n) is 10 years. Plugging these values into the formula, we get PVA = $1,000 x [(1 - (1 + 0.05)^(-10)) / 0.05]. The calculated present value is $8,513.63.

The present value represents the current worth of future cash flows, considering the time value of money. In this case, it reflects the amount you would be willing to invest today to receive a series of $1,000 payments annually for 10 years, given the 5% interest rate. The concept of present value is fundamental in finance and investment decisions, allowing individuals to assess the current value of future cash flows and make informed choices based on the time preferences for money.

Answer 2

The present value of the $1,000 per year annuity for 10 years at a 5% interest rate is $7,360.25, calculated by discounting future cash flows back to present value terms using the time value of money formula.

Step-by-step explanation:

The present value of the annuity can be calculated using the formula for the present value of an ordinary annuity, which is
`PV = PMT * [(1 - (1 + r)^(-n)) / r],` where PV is the present value, PMT is the annual payment, r is the interest rate per period, and n is the number of periods.

In this case, the annual payment (PMT) is $1,000, the interest rate (r) is 5% or 0.05, and the number of periods (n) is 10. Plugging these values into the formula, we get
`PV = $1,000 * [(1 - (1 + 0.05)^(-10)) / 0.05], which simplifies to PV = $1,000 * [(1 - 0.613913) / 0.05].`

Calculating further,

However, the question asks for the present value, which should be the value today. Therefore, we need to discount this amount back to present value terms. Considering the time value of money, the present value is
`$7,721.74 / (1 + 0.05)^10 = $7,360.25.` This reflects the current value of the future cash flows, accounting for the 5% interest rate over the 10-year period.