# Calculating Effective Rate in Secondary Market Annuities

Investors often have confusion about the rate of return used in annuities in general and in Secondary Market Annuities in particular. So to clarify a few terms, we’ll walk through Nominal and Effective rate and the concept of Net Present Value and Discounted Cash Flow.

Please note, all our SMA cases are shown with an effective rate. You should also refer to this page about Secondary Market Annuity Rates

## Effective Rate:

Effective rate, Internal Rate of Return, and Annual Percentage Yield are three terms to describe the same thing for these cases. The effective rate is the yield of the series of cash flows, including the investment (negative) and payments (Positive).

You can calculate this using the XIRR function in MS excel or HP handheld calculators, and we use a program called T-Value.

## Nominal Rate

Nominal interest rate is also defined as a stated interest rate. This interest works according to simple interest and does not take into account the compounding periods. So for example, if you have a mortgage with a 4% rate, 4% is the nominal rate, but the actual Effective Rate (Yield) to the mortgage lender will be different, because of the compounding period of the loan.

## Nominal Rate Vs Effective Rate

Effective interest rate, or APY, is a more accurate reflection of the yield of an investment as it includes the compounding periods during a payment plan. It more accurately can be used to compare two investments with different compounding periods like week, month, year etc.

Often times, the stated or nominal interest rate is less than the effective rate. However, the effective rate depicts the true picture of financial payments because it includes the compounding period.

## Interest Rate and Time

As shown in the example below, interest rate is only meaningful in the context of time and the compounding period. Most often, when people say an interest rate it’s with the assumed context of “per year.”

An **annual interest rate** is also called the **nominal interest rate,** or **Annual Percentage Rate (APR)**

There are other compounding periods available however- common options are month, week, or day.

The yield of an investment with compounding other than annual will be different than the nominal rate. This is the **Effective Interest Rate, **or **Annual Percentage Yield (APY).**

## Time Value of Money Example

Discounted cash flows involve the concept of Time Value of Money- a dollar tomorrow is worth less than a dollar today. How much less? That requires the ‘Discount Rate’ to calculate, and discount rate and effective rate are synonymous for these investments.

$100 in 1 year at a 10% discount rate will cost $90.91 today. A $90.91 investment today at a 10% Effective rate with annual compounding will yield $100 in 1 year. The annual compounding is critical- the nominal and effective rate are both 10% in this example, with annual compounding.

But if monthly compounding is used, the investment is the same $90.91, the Effective (APY) is the same 10%, but the Nominal rate, or APR, is 9.56%

The Effective Interest rate is also equivalent to the Internal Rate of Return, or IRR. To calculate in MS Excel, use the formula XIRR=((payments),(dates),0). This formula calculates the discount rate, or effective rate, or a given series of payments on definite dates. XNPV may also be used to solve for the purchase price of a series of payments on definite dates at a known discount rate.

Please note, all our SMA cases are shown with an effective rate. You should also refer to this page about Secondary Market Annuity Rates where you can download example illustrations in Excel an see a video of how these payments are calculated.

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