What will decrease the present value of an annuity

Recall, the future value FV as the value of an investment after a certain period of time. Future value considers the initial amount invested, the time period of earnings, and the earnings interest rate in the calculation. For example, a bank would consider the future value of a loan based on whether a long-time client meets a certain interest rate return when determining whether to approve the loan.

To determine future value, the bank would need some means to determine the future value of the loan. The bank could use formulas, future value tables, a financial calculator, or a spreadsheet application. The same is true for present value calculations.

Due to the variety of calculators and spreadsheet applications, we will present the determination of both present and future values using tables. In many college courses today, these tables are used primarily because they are relatively simple to understand while demonstrating the material.

For those who prefer formulas, the different formulas used to create each table are printed at the top of the corresponding table. In many finance classes, you will learn how to utilize the formulas. Regarding the use of a financial calculator, while all are similar, the user manual or a quick internet search will provide specific directions for each financial calculator. As for a spreadsheet application such as Microsoft Excel, there are some common formulas, shown in Figure.

In addition, Appendix C provides links to videos and tutorials on using specific aspects of Excel, such as future and present value techniques. Since we will be using the tables in the examples in the body of the chapter, it is important to know there are four possible table, each used under specific conditions Figure. To use the correct table, the bank needs to determine whether the customer will pay them back at the end of the loan term or periodically throughout the term of the loan.

Choosing the correct table to use is critical for accurate determination of the future value. The application in other business matters is the same: a business needs to also consider if they are making an investment with a repayment in one lump sum or in an annuity structure before choosing a table and making the calculation. In the tables, the columns show interest rates i and the rows show periods n. The interest columns represent the anticipated interest rate payout for that investment.

Interest rates can be based on experience, industry standards, federal fiscal policy expectations, and risk investment. Periods represent the number of years until payment is received. The intersection of the expected payout years and the interest rate is a number called a future value factor. The future value factor is multiplied by the initial investment cost to produce the future value of the expected cash flows or investment return.

A lump sum payment is the present value of an investment when the return will occur at the end of the period in one installment. For example, you are saving for a vacation you plan to take in 6 years and want to know how much your initial savings will yield in the future. Future Value of an Ordinary Annuity An ordinary annuity is one in which the payments are made at the end of each period in equal installments. A future value ordinary annuity looks at the value of the current investment in the future, if periodic payments were made throughout the life of the series.

How much would your investment be worth in the future meeting these criteria? In this case, you would use the Future Value of an Ordinary Annuity table.

Multiplying the factor by the amount of the cash flow yields a future value of these installment savings of Determine the future value for each of the following situations. Use the future value tables provided in Appendix B when needed, and round answers to the nearest cent where required. Use FV of an ordinary annuity table. For example, a bank might consider the present value of giving a customer a loan before extending funds to ensure that the risk and the interest earned are worth the initial outlay of cash.

Similar to the Future Value tables, the columns show interest rates i and the rows show periods n in the Present Value tables.

Periods represent how often interest is compounded paid ; that is, periods could represent days, weeks, months, quarters, years, or any interest time period. For our examples and assessments, the period n will almost always be in years. The intersection of the expected payout years n and the interest rate i is a number called a present value factor. The present value factor is multiplied by the initial investment cost to produce the present value of the expected cash flows or investment return.

As with the future value tables, choosing the correct table to use is critical for accurate determination of the present value. When referring to present value, the lump sum return occurs at the end of a period. A business must determine if this delayed repayment, with interest, is worth the same as, more than, or less than the initial investment cost. If the deferred payment is more than the initial investment, the company would consider an investment.

As mentioned, to determine the present value or future value of cash flows, a financial calculator, a program such as Excel, knowledge of the appropriate formulas, or a set of tables must be used. Though we illustrate examples in the text using tables, we recognize the value of these other calculation instruments and have included chapter assessments that use multiple approaches to determining present and future value.

Knowledge of different approaches to determining present and future value is useful as there are situations, such as having fractional interest rates, 8. As discussed previously, annuities are a series of equal payments made over time, and ordinary annuities pay the equal installment at the end of each payment period within the series.

This yields a present value factor of 4. The current value of the cash flow each period is calculated as 4. Our focus has been on examples of ordinary annuities annuities due and other more complicated annuity examples are addressed in advanced accounting courses.

Remember that the units are important: the units on n must be consistent with the units of the interest rate i. Solving for n : This formula allows you to figure out how many periods are needed to achieve a certain future value, given a present value and an interest rate. Variables, such as compounding, inflation, and the cost of capital must be considered before comparing interest rates.

Discuss the differences between effective interest rates, real interest rates, and cost of capital. The amount of interest you would have to pay on a loan or would earn on an investment is clearly an important consideration when making any financial decisions.

However, it is not enough to simply compare the nominal values of two interest rates to see which is higher.

The reason why the nominal interest rate is only part of the story is due to compounding. Since interest compounds, the amount of interest actually accrued may be different than the nominal amount. The last section went through one method for finding the amount of interest that actually accrues: the Effective Annual Rate EAR.

The EAR is a calculation that account for interest that compounds more than one time per year. It provides an annual interest rate that accounts for compounded interest during the year. If two investments are otherwise identical, you would naturally pick the one with the higher EAR, even if the nominal rate is lower. Interest rates are charged for a number of reasons, but one is to ensure that the creditor lowers his or her exposure to inflation.

Inflation causes a nominal amount of money in the present to have less purchasing power in the future. Expected inflation rates are an integral part of determining whether or not an interest rate is high enough for the creditor. The Fisher Equation is a simple way of determining the real interest rate, or the interest rate accrued after accounting for inflation. To find the real interest rate, simply subtract the expected inflation rate from the nominal interest rate. Fisher Equation : The nominal interest rate is approximately the sum of the real interest rate and inflation.

For example, suppose you have the option of choosing to invest in two companies. Thus, Company 2 is the better investment, even though Company 1 pays a higher nominal interest rate. Another major consideration is whether or not the interest rate is higher than your cost of capital. The cost of capital is the rate of return that capital could be expected to earn in an alternative investment of equivalent risk.

Many companies have a standard cost of capital that they use to determine whether or not an investment is worthwhile. In theory, a company will never make an investment if the expected return on the investment is less than their cost of capital. The value of money and the balance of the account may be different when considering fractional time periods. Calculate the future and present value of an account when a fraction of a compounding period has passed. Up to this point, we have implicitly assumed that the number of periods in question matches to a multiple of the compounding period.

That means that the point in the future is also a point where interest accrues. But what happens if we are dealing with fractional time periods? Compounding periods can be any length of time, and the length of the period affects the rate at which interest accrues. Suppose the compounding period is one year, starting January1, If the problem asks you to find the value at June 1, , there is a bit of a conundrum. The last time interest was actually paid was at January 1, , but the time-value of money theory clearly suggests that it should be worth more in June than in January.

In the case of fractional time periods, the devil is in the details. The question could ask for the future value, present value, etc. You can plug in a fractional time period to the appropriate equation to find the FV or PV.

It is the same as that number, but more broadly, is the cost of not having the money for a time period. Since there is still a cost to not having the money for that fraction of a compounding period, the FV still rises. The question could alternatively ask for the balance of the account.

In this case, you need to find the amount of money that is actually in the account, so you round the number of periods down to the nearest whole number assuming one period is the same as a compounding period; if not, round down to the nearest compounding period.

Even if interest compounds every period, and you are asked to find the balance at the 6. The last time the account actually accrued interest was at period 6; the interest for period 7 has not yet been paid.

When borrowing money to be paid back via a number of installments over time, it is important to understand the time value of money and how to build an amortization schedule. When lending money or borrowing, depending on your perspective , it is common to have multiple payback periods over time i.

In these situations, an amortization schedule will be created. This will determine how much will be paid back each period, and how many periods of repayment will be required to cover the principal balance.

This must be agreed upon prior to the initial borrowing occurs, and signed by both parties. This makes it easier for you to plan for your future and make smart financial decisions. An annuity is a contract you enter into with a financial company where you pay a premium in exchange for payments later on. The present value of an annuity is the cash value of all of your future annuity payments.

The rate of return or discount rate is part of the calculation. Thus, the higher the discount rate, the lower the present value of the annuity is. The present value of an annuity is based on the time value of money. With an annuity, you might be comparing the value of taking a lump sum versus the annuity payments. Calculating the present value of annuity lets you determine which is more valuable to you.

As you may have guessed from the number of variables in the formula, calculating the present value of an annuity can be tricky.