compound interest formula
The compound interest formula is used to calculate the amount of money earned or paid on an initial principal amount, which includes both the principal and the accumulated interest over a specific period of time
The compound interest formula is used to calculate the amount of money earned or paid on an initial principal amount, which includes both the principal and the accumulated interest over a specific period of time. The formula is:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment/loan, including interest
P = the principal amount (initial investment or loan)
r = the annual interest rate (expressed as a decimal)
n = the number of times that interest is compounded per year
t = the number of years the money is invested or the length of the loan term
Let’s break down the formula:
1) Start with the principal amount (P).
2) Add 1 to the annual interest rate (r) divided by the number of times interest is compounded per year (n).
3) Raise the result from step 2 to the power of the number of times interest is compounded per year (n) multiplied by the number of years (t).
4) Multiply the result from step 3 by the principal amount (P) to get the future value (A).
For example, let’s say you deposit $1000 in a bank account with an annual interest rate of 5% compounded semi-annually for 3 years. Using the compound interest formula, we can calculate the future value:
P = $1000
r = 5% or 0.05 (expressed as a decimal)
n = 2 (since interest is compounded semi-annually)
t = 3 years
A = 1000(1 + 0.05/2)^(2 * 3)
= 1000(1 + 0.025)^6
= 1000(1.025)^6
= 1000(1.1606)
≈ $1160.60
Therefore, after 3 years, the future value of your initial $1000 deposit will be approximately $1160.60 with compound interest.
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