Single Sum (Lump Sum)

5 formulas

Single sum formulas calculate the future or present value of a one-time lump sum investment. These are the building blocks of time value of money — understanding how a single deposit grows with compound interest over time, or how to discount a future amount back to today's dollars.

Lump Sum

Calculates the future value of a single present amount invested at a fixed annual interest rate.

FV = PV \times (1 + k)^n

Showing future value, annual

4 ways to solve · 3 compounding methods

Simple Interest

Interest earned on the original principal only, with no interest on interest: principal times rate times time. Used for short-term loans, some bonds' accrued interest, and as the baseline that compound interest is measured against.

I = PV \times k \times n

Discount Factor

The present value of one unit of currency received n years from now at rate k. Multiply any future cash flow by its discount factor to get its value today.

DF = \frac{1}{(1 + k)^n}

Compound Annual Growth Rate (CAGR)

The single annual rate that would take a beginning value to an ending value over n years with annual compounding. It smooths a lumpy path into one comparable growth figure.

CAGR = \left(\frac{V_{\text{end}}}{V_{\text{begin}}}\right)^{1/n} - 1

Rule of 72 (Doubling Time)

A mental-arithmetic estimate of how many years it takes money to double at a given annual rate: 72 divided by the rate in percent. Accurate to within a few months for rates between roughly 4% and 12%.

n_{\text{double}} \approx \frac{72}{100 \, k}