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Understand How to Solve Problems Related to Annuities

An annuity is a series of equal payments that a financial institution makes to an investor; these payments are made at the end of each period (usually a month or a year) for a specific number of years. To set up an annuity, an investor and a financial institution (for example, an insurance company) sign a contract in which the investor agrees to transfer a specific amount of money to the financial institution and the financial institution, in turn, agrees to pay the investor a set amount of money at the end of each period for a specific number of years.

To determine the set amount of each equal payment for a certain investment, you must know the amount of the investment (PV), the interest rate (I), and the number of years the annuity will last (N).

Problem 4: Annuities

When you retire at age sixty, you have $750,000 in your retirement fund. The financial institution you have invested your money with will pay you an interest rate of 7 percent. Assuming you live to age ninety, you will need to receive payments for thirty years after you retire. How much can you expect to receive each year for your $750,000 investment with a 7 percent interest rate?

To solve this problem, input the following information in your financial calculator:

Set –$750,000 as your present value (PV). Your present value is negative because it is considered an outflow. You pay this amount to the financial institution, and the financial institution pays you back with annual payments.

Set thirty as the number of years (N).

Set 7 percent as your interest rate (I). Remember to convert this percentage to the decimal 0.07.

Now solve for the payment (PMT). The present value of this annuity is $60,439.80. This means that you should receive thirty annual payments of $60,439.80.

Without a financial calculator, solving this problem is a bit trickier. The formula is as follows:

PMT = PVn,i/[1 – (1/(1 + i)n )]/i

PMT = $750,000/[1 – (1/(1.07)30)]/0.07 = $60,440

The key is to start saving for retirement as soon as you can. Starting to save early will make a big difference in what you are able to retire with.

Compound Annuities

A compound annuity is a type of investment in which you deposit a set sum of money into an investment vehicle at the end of each year; you deposit this amount for a specific number of years and allow that money to grow.


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