You have a chance to buy an annuity that pays $5,000 at the beginning of each year for 5 years. You could earn 4.5% on your money in other investments with equal risk. What is the most you should pay for the annuity?

The maximum amount that I will pay to purchase this annuity will be $22440.

Explanation:

The amount $5000 is the amount that I am paid in the start of the year which is just after the purchase of the annuity.

At the end of year 1, I will be paid $5000 and likewise at the end of year 2, 3 and year 4. So the annuity factor that we must calculate is for 4 number of years, which is n.

The annuity formula is attached with the answer.

By putting the value of n and r, we have:

Present Value = $5000 * (1-(1+4.5%)^4) / 4.5%  = $5000 * 3.588 = $17940

The amount $17940 includes 4 yearly payment and does not includes the initial year payment made at the start of the year.

So the amount received in the year zero will be added to calculate the maximum amount that an investor must pay to purchase this annuity.

Maximum amount that should be paid = $17940 + $5000 = $22440

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