Reverse Compound Interest Calculator

Reverse calculator

Work backwards from a future target

Use this simple reverse calculator to estimate the starting amount needed today to reach a future target, assuming a fixed annual return and compounding frequency.

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Target amount

Annual interest rate

%

Years

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Rate conventionNominal annual rateEffective annual rate (AER/APY)

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Formula used

The calculator rearranges the compound interest formula. Instead of calculating future value from a starting amount, it divides the target future value by the growth factor.

Present value = Future value / (1 + r/n)^(n × t)

An effective annual rate uses Present value = Future value / (1 + r)^t. For continuous compounding of a nominal rate it uses Present value = Future value / e^(r × t).

How to work backwards with compound interest

The forward formula is A = P × (1 + r/n)^(n × t). To find the original deposit, divide both sides by the same growth factor:

P = A / (1 + r/n)^(n × t)

• A is the target future balance; P is the starting balance you want to find.
• r is the nominal annual rate as a decimal: 5% is 0.05.
• n is the number of compounding periods per year: 1 for annual or 12 for monthly.
• t is the number of years. Keep the rate and period units consistent.

These examples assume a constant rate, no further deposits or withdrawals, and no fees or tax. They are mathematical estimates, not guaranteed returns.

Example 1: find an original deposit from an annual balance

A balance is worth £10,000 after three years at 5% compounded annually. What was the starting deposit?

1. Set A = 10000, r = 0.05, n = 1 and t = 3.
2. Calculate the growth factor: 1.05^3 = 1.157625.
3. Divide the final balance by that factor: P = 10000 / 1.157625.

The original deposit is approximately £8,638.38. Check it by multiplying the unrounded answer by 1.05^3: it returns £10,000. Subtracting 15% from £10,000 would be incorrect because each year's interest grew from a different balance.

Example 2: a £25,000 target with monthly compounding

You want £25,000 in ten years at a nominal annual rate of 5%, compounded monthly, with no further deposits.

1. Monthly rate: 0.05 / 12. Number of periods: 12 × 10 = 120.
2. Growth factor: (1 + 0.05/12)^120, approximately 1.6470095.
3. Starting balance: 25000 / (1 + 0.05/12)^120, approximately £15,179.03.

Keep full precision while calculating and round only the final displayed amount. If you need a minimum deposit in whole pennies that reaches or exceeds the target under the model, round the exact required deposit up to the next penny rather than rounding to the nearest penny.

Finding the starting amount is not the same as finding the rate

This calculator assumes you already know the rate and solves for the starting amount. If the starting and final balances are known instead, with no payments in between, the nominal rate for a specified compounding frequency is r = n × ((A/P)^(1/(n × t)) − 1), for positive balances and a term greater than zero. Multiply the result by 100 to express it as a percentage. Payments during the term require a different calculation.

Saving regularly instead? Use the monthly savings goal calculator to solve for the contribution, or practise with the reverse compound interest worksheets.