The future value of an annuity is a fundamental concept in finance. However, there are some details and distinctions that can make a big difference in the future value of an annuity.

Watch the video and answer the question that follows.

Consider an ordinary annuity that pays out over 4 as well as an annuity due that also pays out over 4 periods. Assume that each of these annuities has the same interest rate.

The ordinary annuity will have a smaller future value as the annuity due, because the ordinary annuity has fewer periods of earning interest when compared to the annuity due.

Read the following text and answer the questions that follow.

An annuity is a series of payments of fixed amounts that occur at regular intervals for a specific period of time. Recall from the previous stage of the problem that if these payments happen at the beginning of each period, the annuity is an annuity due. If the payments happen at the end of each period the annuity is an ordinary annuity. In practice, ordinary annuities are more commonly used.

The future value of an annuity is the amount of cash you will have at the end of the life of the annuity. In other words, it is the amount to which the annuity payments will grow over a given period of time, if those payments can be compounded with an given interest rate. Given the interest rate I, the amount per fixed payment PMTPMT, and the number of periods N, the future value of an ordinary annuity (FVANFVA) can be calculated as:

FVAN=PMT(1+I)(N-1)+PMT(1+I)(N-2)+PMT(1+I)(N-3)+...+PMT(1+I)0FVA=PMT(1+I)N-1+PMT(1+I)N-2+PMT(1+I)N-3+...+PMT(1+I)0

Which simplifies to:

FVAN=PMT((1+I)N1I)FVA=PMT1+1

While in practice this calculation is typically done on a financial calculator or spreadsheet application, this equation can be useful when solving annuity problems without those resources.

When using a financial calculator to solve for the future value of an ordinary annuity, it is important to keep in mind the following:

The PV (present value) is the amount of funds at the start. For an ordinary annuity in isolation, this will be 0.The PMT is entered as a negative number when it is a cash outflow.The I/YR is entered as a number, such as 10 for 10 percent, not as a decimal such as 0.10 for 10 percent.

Note that financial calculators typically calculate the future value of an ordinary annuity by default, but can easily be adjusted to calculate the future value of an annuity due as well.

A financial calculator can also be used to calculate the other components of an annuity, given all the values of the other components. For example, given the PV, I/YR, N, and FV, a financial calculator can solve for the period payment PMT.

Question #1 True or False: I/YR is always entered as a decimal that is less than 1 when solving annuity problems.

True

False

Suppose you know want to solve for the PMT of an ordinary annuity using a financial calculator.

#2 In order to solve for the PMT of an ordinary annuity, which of the following components will you need to know the value of? Check all that apply.

N

I/YR

FV

PV

Step 2: Learn: Future Value of an Annuity

Using a financial calculator is a common way of finding the future value of an ordinary annuity.

Watch the video and then answer the questions that follow.

Suppose that Megan is 45 years old and has no retirement savings. She wants to begin saving for retirement, with the first payment coming one year from now. She can save $20,000 per year and will invest that amount in the stock market, where it is expected to yield an average annual return of 12.00% return. Assume that this rate will be constant for the rest of hers life. In short, this scenario fits all the criteria of an ordinary annuity.

Megan would like to calculate how much money she will have at age 60.

Use the following table to indicate which values you should enter on your financial calculator. For example, if you are using the value of 1 for N, use the selection list above N in the table to select that value.

Input15 12.00% 0-$20,000 KeystrokeNI/YPVPMTFVOutput ?

Using a financial calculator yields a future value of this ordinary annuity to be approximately $745,594.29 at age 60.

Megan would now like to calculate how much money she will have at age 65.

Use the following table to indicate which values you should enter on your financial calculator. For example, if you are using the value of 1 for N, use the selection list above N in the table to select that value.

Input20 12.00% 0-$20,000 KeystrokeNI/YPVPMTFVOutput ?

Using a financial calculator yields a future value of this ordinary annuity to be approximately at age 65.

Megan expects to live for another 30 years if she retires at age 60, with the same expected percent return on investments in the stock market.

She would like to calculate how much she can withdraw at the end of each year after retirement.

Use the following table to indicate which values you should enter on your financial calculator in order to solve for PMT in this scenario. For example, if you are using the value of 1 for N, use the selection list above N in the table to select that value.

Input30 12.00% Amount saved for retirement by age 60 0KeystrokeNI/YPVPMTFVOutput ?

Using a financial calculator, you can calculate that Megan can withdraw at the end of each year after retirement (assuming retirement at age 60), assuming a fixed withdrawal each year and $0 remaining at the end of her life.

Megan expects to live for another 25 years if she retires at age 65, with the same expected percent return on investments in the stock market.

Use the following table to indicate which values you should enter on your financial calculator. For example, if you are using the value of 1 for N, use the selection list above N in the table to select that value.

Input25 12.00% Amount saved for retirement by age 65 0KeystrokeNI/YPVPMTFVOutput ?

Using a financial calculator, you can calculate that Megan can withdraw at the end of each year after retirement at age 65, assuming a fixed withdrawal each year and $0 remaining at the end of her life.

Step 3: Practice: Future Value of an Annuity

Now its time for you to practice what youve learned.

Suppose that Megan is 45 years old and has no retirement savings. She wants to begin saving for retirement, with the first payment coming one year from now. She can save $12,000 per year and will invest that amount in the stock market, where it is expected to yield an average annual return of 4.00% return. Assume that this rate will be constant for the rest of hers life.

Megan would like to calculate how much money she will have at age 60.

Using a financial calculator yields a future value of this ordinary annuity to be approximately at age 60.

Megan would now like to calculate how much money she will have at age 65.

Using a financial calculator yields a future value of this ordinary annuity to be approximately at age 65.

Megan expects to live for another 30 years if she retires at age 60, with the same expected percent return on investments in the stock market.

Using a financial calculator, you can calculate that Megan can withdraw at the end of each year after retirement (assuming retirement at age 60), assuming a fixed withdrawal each year and $0 remaining at the end of her life.

Megan expects to live for another 25 years if she retires at age 65, with the same expected percent return on investments in the stock market.

Using a financial calculator, you can calculate that Megan can withdraw at the end of each year after retirement at age 65, assuming a fixed withdrawal each year and $0 remaining at the end of her life.