# How to Calculate a Lump Sum Plus Interest Rate

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One of the questions you will be asked when you sign up for your retirement plan or annuity is how you would like your distributions. You can either take them as a lump sum or as payments over time. What would happen if you took the lump sum and put it in an investment that would pay a certain interest rate over time? The lump-sum formula will let you calculate the future value of the money if you took this action. Let’s see how to build a lump sum calculator.

## Lump-Sum Formula

The first thing you need to know is whether you will earn simple interest or compound interest. If you invest the lump sum and do not set it up so that the earnings are reinvested, you will use the simple interest formula where FV is the future value of the money.

FV = P(1+r)

FV = future value of the money after the given time period

P = principal or initial lump sum amount

r = the annual rate of return

Using this formula, ​\$100​ invested at an annual rate of ​4 percent​ would be equal to ​\$104​ in one year. In year ​two​, it would be worth ​\$108​.

If you were to reinvest the interest that you earned, the interest is calculated on the initial investment plus any interest earned so far. It uses the formula:

FV = P (1+r/n)^nt

In this case, “t” is the number of years the principal is invested and “n” represented the number of periods the interest is calculated during the year. This can be monthly, in which case n=​12​. If it is calculated quarterly, n=​4​ and for annual compounding, n=​1​.

## Lump-Sum Formula Examples

Let’s say you took this same ​\$100​ and reinvested the interest every year for ​five​ years and that it is compounded monthly. The formula would look like this.

FV = (100 (1 + .04/12))^12(5)

FV = \$122.10

By comparison, you would only have ​\$120​ after ​five​ years if you did not reinvest the interest.

Let's use the lump-sum calculator to see how much a lump-sum payment from an annuity would be worth if you invested the amount at ​7 percent​ and reinvested the interest for ​20​ years. How much would you have every year in interest? Let’s assume a principal of ​\$100,000​ for simplicity.

Using the lump-sum formula, this gives you an additional ​\$7,000​ in the first year, which is an extra ​\$583​ per month. If you did not take the money out and set it up to reinvest, in ​20​ years, you would have a total of ​\$386,968​ total if it is compounded annually. If this same amount is compounded monthly for the same amount of time, you would earn ​\$403,873​.

## Lump-Sum Cash Flow

Now that you understand how the compounding calculator works for a lump-sum annuity, you can find a compound interest calculator that can help you visualize your savings growth. One of the ways you can use this formula is to see how much you will need to generate a certain income per month.

How much would you need to generate ​\$1,000​ per month at ​7 percent?​ If you wanted to generate an extra ​\$1,000​ per month in income from interest, you would need a lump-sum payment of ​\$104,685​ to generate this extra income. This amount compounded annually without reinvestment would earn an additional ​\$12,013​ per year.

Another thing to consider is that you might need to deduct the taxes you will owe. You can find many of these answers in this IRS guide to taxes for retirees.