Future value formula:
what a single deposit becomes with compounding

The question future value answers

If you put a fixed amount away today and leave it untouched, what will it be worth on a later date? That is the question future value (FV) answers. It needs only the starting amount, the rate of return per period and the number of periods.

The result is larger than the original because earnings are added back to the balance and then earn returns of their own. This is compounding, and it is why a ten-year deposit at 8% does not just add ten simple instalments of 8% of the starting amount. Interest on interest is what separates compound growth from simple interest.

It also helps to separate three things that get blurred in conversation: the principal you put in, the interest you earn, and the future value, which is the two added together. A bank statement may show only the last, an offer letter may emphasise the middle one, and a plan needs all three to be compared fairly.

Future value is a projection. It assumes the rate stays fixed and that nothing is added or withdrawn, which is a fair description of a bank term deposit and a rough one for market investments.

The formula and its parts

The two inputs people most often get wrong are r and n. They must be expressed in the same time unit. A 9% yearly rate compounded quarterly is 2.25% per quarter, and ten years is 40 quarters. Using 9% with 40 periods overstates the result, and using 2.25% with 10 periods understates it.

Solving the same equation in other directions is useful too. The rate needed to turn PV into a target FV over n periods is (FV ÷ PV)^(1/n) − 1, and the number of periods is ln(FV ÷ PV) ÷ ln(1 + r).

Worked example: ₹1,00,000 at 8% for 10 years

Simple interest at the same 8% would have added only ₹80,000 over ten years, giving ₹1,80,000. The extra ₹35,892 is the effect of compounding alone.

A quick way to sense-check: at 8%, money roughly doubles in nine years, so ten years should land a little above ₹2,00,000. The answer fits.

How compounding frequency changes the answer

When interest is credited more often, each credit starts earning sooner. The stated annual rate stays at 8%, but the effective yield rises a little for each step in frequency.

The gap between yearly and monthly is about ₹6,072, or 2.8% of the final value. Moving from monthly to daily adds just ₹571 more. The limit, continuous compounding with FV = PV × e^(rt), is ₹2,22,554, so there is a ceiling on how much frequency can add.

Reading a real deposit quote

Banks quote a nominal yearly rate and a compounding schedule, and the two together fix the maturity value. Take a three-year deposit of ₹2,50,000 at 7.1% a year with interest compounded quarterly. The quarterly rate is 7.1% ÷ 4 = 1.775% and there are 12 quarters.

The ₹1,649 difference between the two is small on this size of deposit, but it shows why two products with the same headline rate can pay different amounts. Check whether your deposit pays interest at maturity, which compounds, or pays it out periodically, which does not.

Why the headline number can mislead

• Inflation: ₹2,15,892 in ten years buys less than ₹2,15,892 does today. At 6% inflation, the same amount has the purchasing power of about ₹1,20,550 in today's money (₹2,15,892 ÷ 1.06¹⁰ = ₹2,15,892 ÷ 1.7908).
• Taxes and charges: interest is often taxable and funds charge fees, so the figure you keep is below the formula's result. Check the current rules for your product.
• Variable returns: market investments do not earn a steady 8%. The formula gives an average-case illustration, not a promise.
• Rate quoting: nominal, effective and compounding frequency all have different meanings. Always confirm what the quoted rate refers to.

Turning the formula around: rate and time

Sometimes the target is known and the unknown is the rate or the waiting time. Rearranging the equation handles both, as long as the amounts are positive.

• Required yearly rate: (FV ÷ PV)^(1 ÷ n) − 1. To double ₹1,00,000 in 8 years you need 2^(1/8) − 1 = 9.05% a year.
• Required time: ln(FV ÷ PV) ÷ ln(1 + r). To reach ₹5,00,000 from ₹1,00,000 at 8% you need ln 5 ÷ ln 1.08 = 20.9 years.

Those two results are worth remembering as sanity checks. A target that needs a rate far above what is realistic is a signal to extend the time, add regular deposits, or lower the goal.

The last row shows how patient compounding behaves: the second decade added about ₹2.5 lakh to the first decade's ₹1.16 lakh, and the third decade added more than ₹5.4 lakh. Time does the heavy lifting once the balance is large.

Using a calculator to test scenarios

The value of a calculator here is trying alternatives: what if the rate is 7% instead of 8%, or the time is 12 years instead of 10? Changing one input at a time shows which one has the larger effect. For lump sums held a long time, adding two years is usually worth more than gaining one percentage point of rate.