Compound interest is a widely used financial concept. It refers to the process of earning interest on both the principal amount and any accumulated interest. Continuous compound interest is a type of compound interest that is calculated and added to the principal amount continuously, rather than at specific intervals. This means that the interest is compounded an infinite number of times per year. The continuous compound interest formula is used to calculate this continuous compound interest.
Formula and Use
The continuous compound interest formula shows the interest accumulated at the end of a time (n) on an amount (PV) deposited today and compounded continuously at an interest rate (i).
In the formula the terms have the following meanings
PV (Initial Principal Amount) PV represents the initial principal amount that is invested. This can be any amount of money that is initially invested in an account, such as a savings account, CD, or other investment vehicle.
i (Interest Rate) i represents the annual interest rate, expressed as a decimal. For example, if an investment has an annual interest rate of 5%, i would be equal to 0.05. It’s important to realize that the interest rate used in the formula should be the annual interest rate.
n (Time Period in Years) n represents the time period, expressed in years, for which the investment is held. For example, if an investment is held for 5 years, n would be equal to 5.
Example 1 Using the Continuous Compound Interest Formula
If an amount of 7,000 is deposited at time zero (today) and is compounded continuously for a period of 4 years at an an interest rate of 5%, then the compound interest at the end of year 4 is given by the continuous interest formula as follows:
PV = 7,000 i = 5% n = 4 Compound interest = PV x (ein - 1) Compound interest = 7000 x (e(5% x 4) - 1) Compound interest = 1,549.82
Example 2 Using the Continuous Compound Interest Formula
If an amount of 4,000 is deposited at time zero (today) and is compounded continuously for a period of 24 months at an an interest rate of 6%, then the compound interest at the end of month 24 is given by the formula as follows:
PV = 4,000 i = 6% n = 24/12 = 2 years Compound interest = PV x (ein - 1) Compound interest = 4000 x (e(6% x 2) - 1) Compound interest = 509.99
The continuous compound formula is one of many formulas used in time value of money calculations. Discover another at the links below.