A(t) = P (1+r/n) ^nt
The equation A(t) = P(1+r/n)^nt represents the formula for compound interest, where:
– A(t) represents the amount of money at time t after interest has been applied
The equation A(t) = P(1+r/n)^nt represents the formula for compound interest, where:
– A(t) represents the amount of money at time t after interest has been applied.
– P represents the principal, which is the initial amount of money invested.
– r represents the interest rate (expressed as a decimal).
– n represents the number of times interest is compounded per time period.
– t represents the number of time periods (e.g., years) that have passed.
To understand how this formula works, let’s break it down:
1. P(1+r/n)^(nt):
– (1+r/n) represents the growth factor. It is calculated by adding 1 to the interest rate divided by the number of compounding periods.
– nt represents the total number of compounding periods.
2. P(1+r/n)^(nt): This term calculates the amount of money accumulated without considering any interest earned. It represents the principal P multiplied by the growth factor to the power of the total number of compounding periods.
3. A(t): This is the final result and represents the accumulated amount of money at time t, including the interest earned.
Example: Let’s say you invest $5,000 at an annual interest rate of 5% compounded quarterly (n=4) for 3 years (t=3).
Using the given formula, we have:
A(t) = 5000(1+(0.05/4))^(4*3)
Simplifying further:
A(t) = 5000(1+0.0125)^(12)
Calculating the growth factor:
A(t) = 5000(1.0125)^(12)
Using a calculator, we find:
A(t) ≈ 5000(1.159274074) ≈ $5,796.37
So, after 3 years, the accumulated amount would be approximately $5,796.37.
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