Future value and compound interest

Money has a time value: 1,000 today is worth more than 1,000 next year, because today's 1,000 can be invested and earn a return in the meantime.

With compound interest, each year's interest is added to the balance, so next year you earn interest on the interest too. Over long periods, that difference becomes large.

Simple interest grows in a straight line, adding the same 600 every year. Compounding curves upward, because each year's 6% is earned on a larger balance. After 30 years the compound balance is 57,435, against 28,000 with simple interest.

A quick sense-check: the rule of 72. Dividing 72 by the interest rate in percent gives a rough number of years for money to double. At 6%, 72 ÷ 6 = 12 years; the exact answer, from solving 1.06ⁿ = 2, is 11.9 years. It is an approximation that works best for rates between about 4% and 12%, but it is a handy way to spot a figure that is wildly off before you rely on it.

How it is used at work. A fictional company, Rimal Printing, puts aside SAR 400,000 today to replace a press in 5 years, in a deposit paying 4.5% a year. Compounding tells the finance team the fund will hold SAR 498,473 by then, so they can compare it with the expected price of the new press and see whether they need to add more now. The same arithmetic projects revenue at an assumed growth rate, or the amount owed on a loan if nothing is repaid.

What the formula assumes. One constant rate, applied once per period, with nothing added or withdrawn. Real investments rarely earn a steady rate, so FV at an expected return is an estimate, not a promise. And if interest is credited more often than once a year, the rate and the number of periods must both be expressed per period, which is the subject of the effective-rates lesson.

Modeling it year by year

In a model you rarely type the final number. You build a schedule where each year's closing balance becomes the next year's opening balance, and every figure links back to the assumption cells. Change an assumption, and the whole schedule updates.

Solving for the rate

Rearranging FV = PV × (1 + r)ⁿ gives the compound annual growth rate needed to turn PV into FV in n years: r = (FV ÷ PV)^(1/n) − 1. The worksheet function RRI(n, PV, FV) does the same.