Question

Your friend offers to pay you an annuity of $4,000 at the end of

each year for 5 years in return for cash today. You could earn 2.5%
on your money in other investments with equal risk. What is the
mos

Answer 1

Your friend is offering to pay you an annuity of $4,000 at the end of each year for 5 years. To determine if this offer is a good deal.

`Using a calculator, we find that the future value of the $18,422.35 after 5 years is approximately $20,992.65.`

To calculate the present value of the annuity, we need to discount each payment to its present value. We can use the formula for the present value of an ordinary annuity:

`PV = C * (1 - (1 + r)^(-n)) / r`
Where PV is the present value, C is the cash flow (annuity payment), r is the interest rate, and n is the number of periods.

Let's plug in the values:

PV = $4,000 * (1 - (1 + 0.025)^(-5)) / 0.025

Simplifying the equation:

PV = $4,000 * (1 - 1.025^(-5)) / 0.025

FV = PV * (1 + r)^n

FV = $18,422.35 * (1 + 0.025)^5


`Using a calculator, we find that the future value of the $18,422.35 after 5 years is approximately $20,992.65.`
In summary, accepting your friend's offer of $18,422.35 in cash today in exchange for the annuity payments would be a better financial decision compared to earning 2.5% on your money in other investments with equal risk.