Savings Calculator.

Entry Description Amount
Initial Savings:
Monthly Addition:
APR (%):
Years to Invest:
State & Federal Tax Rate:
Inflation:
Total Amount Deposited:
Interest Earned:
Your Savings, Before Taxes:
Income Tax:
Your Savings, After Taxes:
Spending Power of Your Savings:

How To Use This Tool

The Basics

Use this calculator to quickly figure out how much money you will have saved up during a set investment period. First, enter your initial amount you have set aside, then enter the interest rate along with how much money you intend to save each month.

Once you have entered this information select how many years you want to save money for and the calculator will inform you of how much money you will have saved up before income taxes, how much tax you'll owe & what this amount is worth in real terms after accounting for inflation.

Calculation Mechanics

How Interest is Compounded

Interest is compounded monthly. Most bank savings accounts use a daily average balance to compound interest daily and then add the amount to the account's balance monthly, which is mathematically quite similar to monthly compounding.

How Taxes Are Accounted For

This calculator estimates taxes based on the rate entered with the tax payment made at the end of the investment period. This approach is how tax payments would work on savings stored inside a tax deferred retirement account.

Ordinary interest on a regular bank savings account is typically paid for on an annual basis, with banks sending account holders a 1099-INT if they earn above some baseline level of around $10.

How Inflation is Accounted For

After taxes are deducted from interest earnings & final savings are calculated, inflation is accounted for by multiplying the final amount by (100% - inflation rate)years

How to Calculate Compound Interest

The easy way to do this is to use the above calculator. The hard way would be manually calculating the returns.

Single Deposit

The above calculator automatically does this for you, but if you wanted to calculate compound interest manually the formula is

FV = PV * (1 + r/n)nt

Formula definitions:

To find the interest which was earned from the account all you would need to do is subtract the initial deposit amount from the end result.

A Series of Deposits

End of the Month

For recurring monthly deposits where deposits are made at the end of each month you would use the following calculation.

FV = PMT * (((1 + r/n)nt - 1) / (r/n))

All the definitions in this formula are the same as the definitions in the first formula, except PMT is the monthly deposit.

If you want to figure out how much interest was earned then you would simply subtract the payment amount times how many payment cycles were made from the end total.

If you deposited $200 per month for 2 years you would then subtract the $2,400 in deposits from the total to get the interest earned.

Beginning of the Month

If the deposits occur at the beginning of each month you would use the same exact formula, but then add 1 more monthly calculation to it.

FV = PMT * (((1 + r/n)nt - 1) / (r/n)) * (1 + r/n)

Series of Deposits, With Initial Deposit

If you made a series of deposits and there was an initial lump sum deposit then you would treat the series and the initial deposit as two separate entities & then add each total together to get your final savings amount.

Taxes & Inflation

This would be the first step of calculating your returns, then you would need to subtract income taxes from the returns & then account for inflation.

Multiply your interest earned against income tax rate (as a decimal) and that will be the total amount of taxes paid. Subtract that amount from your future savings value to get your savings after taxes.

To account for inflation you would use the following formula

PV = FV * ( 1 - i)n

The present value of a future sum of money is equal to the future value times (1 - the annual rate of inflation as a decimal) raised to the nth power, where n is the number of years into the future.

What if Market Conditions Change?

An Example Change

If you anticipate market conditions changing drastically you can break your calculation into 2 stages. For example, "bond king" Jeffrey Gundlach stated in December 2017 he expected the United States 10-year Treasury yield would hit 6% by 2020.

Significantly higher bond rates would likely force banks to pay investors higher rates of interest to attract capital to high yield savings accounts or CD investments.

Two Options: Estimate Average or Run Multiple Calculations

You could either estimate the average interest rate you will receive during the duration of your investment or you could break your calculation down into 2 stages.

Breaking Down Calculation

Here is an example of the breaking down approach using the following criteria:

The first 2 years calculation results are as follows:

The next 5 years calculation starts with the $22,420.32 as the initial deposit then adjusts term to remaining 5 years at 4.5% interest.

Averaging

The second option would be averaging the rates together to create a blended average rate.

(1.7% * 2 years + 4.5% * 5 years) / 7 years =

3.4 + 22.5 / 7 =

25.9 / 7 = 2.8556%

Which Approach is Better?

Each of these strategies has strengths and weaknesses.

The strength of the second option is seeing estimated spending power of the set final number accounting for the compounded impacts of inflation throughout the entire investment period.

The strength of the first option is it is much quicker to do.

With either approach you are only going to get a rough approximation of performance as market conditions are quite unpredictable. That is plenty good enough in most cases though, because nobody can consistently predict the markets.

Burton G. Malkiel's A Random Walk Down Wall Street is a great book offering wisdom on how one can succeed in volatile markets.