 # Annual Rate Tool For Personal Finance Uses

The annual rate calculator can be very useful for personal financial planning purposes. For example, it can allow you to determine the average minimum rate of return your investments must earn in order for you to reach your retirement goals.

### Instructions:

Change the inputs in the fields above and click “Calculate” to get your result.

#### Present Value:

The lump sum amount with which you are starting, if applicable. So if you are starting with \$85,000, for example, you would enter this amount as a negative. If none, enter zero. Present value should typically be entered as a negative if it represents an amount you will pay to invest, for example, in order to generate a future value.

Future Value:

The lump sum amount which you will have at the end of a specified time period. As an example, if you’re looking to figure out how many years (time period) it will take you to accumulate \$850,000 by retirement, you would enter this number as the future value.

#### Number of Years:

The time period or time horizon, stated in years, which you want to use in your calculation. Similar to the “annual rate” above, this number is automatically adjusted in the calculation based on the compounding frequency selected. For example, let’s say you are computing the present value of a 30 year mortgage loan. You would enter 30 for the number of years. But the compounding periods used in the calculator will be 360 (30 x 12) if you choose “monthly” compounding,” which is the case with mortgage loans.

#### Periodic Payment:

The amount of any payment per compounding period. Enter this number as a negative if you are paying or investing this amount. An example of this would be a contribution or payment to an investment account.

If you are receiving periodic payments, then you would enter this amount as a positive. An example of this would be a withdrawal or payment from a retirement account to you.

You can enter a present value (see above), periodic payments, or both.

Make sure you match the periodic payment with the compounding frequency chosen. For example, if you choose monthly compounding, the periodic payment will be the payment made each month. If you choose quarterly, it will be the total payments you make for each three month period, and so on.

#### Type of Payment:

This input only applies if there are periodic payments. The default value is “End of Period,” which implies payments are made at the end of each compounding period (“in arrears”). But you can also choose to calculate the result as if the payments are made at the beginning of each period (“in advance”).

#### Compounding Frequency:

The frequency with which returns and any periodic payments are added to the running balance on which the rate is applied. For example, with a bank savings account or money market account, the interest compounds monthly. A stock dividend reinvestment plan, on the other hand would compound quarterly since most common stocks pay dividends every three months.

Annual Rate Result:

This can be an average investment return on a portfolio, or an inflation rate, for example. The rate is adjusted automatically in the calculation when you choose the compounding frequency. For example, let’s say you enter 6% as the annual rate and “quarterly” for the compounding frequency. In this case, a periodic rate of 1.5% (6% / 4) will be used in the calculation.

## Average Minimum Rate You Must Earn To Meet Your Goal

Let’s say you are 40 years old and currently have \$90,000 (present value) in your retirement investment accounts. You estimate you will need a nest egg of \$600,000 by retirement at age 65. You contribute \$5,500 (periodic payment) at the end of each year (compounding frequency) into your retirement accounts. How much will you need to earn on average at a minimum in order to meet your goal?

Plug in the criteria above, and you get 5.292%. This is a very reasonable rate to expect from a well balanced investment portfolio.

### The inputs are as follows:

present value: \$-90,000 (this represents the beginning amount you have invested and accumulated in your retirement account(s))

future value: \$600,000 (amount you are aiming to accumulate by retirement)

number of years: 25 (65 years old projected retirement age in this example minus 40 years old current age)

periodic payment: \$-5,500 (the amount you are paying into your investment account(s) each year)

type of payment: “End of Period” (default) – (we’re assuming you make periodic payments at the end of each year in this case)

compounding frequency: Annual (we are assuming you invest your periodic payments and reinvest any accumulated earnings once per year in this example)

## Another Retirement Planning Example

Let’s assume the same criteria as above but instead of 65, you plan to retire at 55 years of age. You also make your contributions to retirement contributions and reinvest any earnings on a quarterly basis (\$5500/4 = \$1375). Plug the numbers in and you get a minimum average rate of 10.225%.

### The inputs are as follows:

present value: \$-90,000 (this represents the beginning amount you have invested and accumulated in your retirement account(s))

future value: \$600,000 (amount you are aiming to accumulate by retirement)

number of years: 15 (55 years old projected retirement age in this example minus 40 years old current age)

periodic payment: \$-1,375 (the amount you are paying into your investment account(s) each quarter or every three months)

type of payment: “End of Period” (default) – (we’re assuming you make periodic payments at the end of each quarter in this case)

compounding frequency: Quarterly (we are assuming you invest your periodic payments and reinvest any accumulated earnings four times each year in this example)

So you see here how the significantly shorter investment time horizon of 15 years requires you to earn more on your investments in order to meet your goal. This may require a much more aggressive allocation to stocks, for example, in your investment portfolio. The more frequent compounding (quarterly vs annually) does help, otherwise the required annual rate would be even higher in this second example.

But you don’t have to necessarily take more risk with an aggressive investment portfolio. For example, you may be able to modify your budget and potentially contribute more each period into your retirement accounts. This will lower the average minimum annual rate you must earn to meet your goal.

## Conclusion

This calculator assumes fixed payments and rate input variables throughout the time horizon used. For something like a fixed rate mortgage, this is not an issue. But for predicting future savings goals and investment returns, it does not allow for more flexible and detailed analysis.

More detailed inputs can be helpful. For example, your asset mix can change as you get closer to retirement (may affect investment rate of return). Or your savings may change based on income or other factors.

But greater detail can also provide a false sense of accuracy. The future is impossible to predict for many variables. For example, you don’t know exactly how much you will be able to save each year, or how much your investments will earn.

Nevertheless, you can use this tool to perform basic finance calculations in an efficient manner.  Using estimated averages for the input variables can give you some useful ballpark figures.