The formula for calculating the amount of money returned for an initial deposit money into a bank account or CD (Certificate of Deposit) is given by
A is the amount of returned.
P is the principal amount initially deposited.
r is the annual interest rate (expressed as a decimal).
n is the compound period.
t is the number of years.
Carry all calculations to 6 decimals on all assignments then round the answer to the nearest cent.
Prt = A
To calculate the amount of money returned for an initial deposit into a bank account or CD, you can use the formula:
A = P(1 + r/n)^(n*t)
Let's break down the formula:
- A represents the amount of money returned.
- P is the principal amount initially deposited.
- r is the annual interest rate, expressed as a decimal (e.g., 5% would be 0.05).
- n is the compound period, which represents the number of times interest is compounded per year (e.g., quarterly would be 4, monthly would be 12).
- t is the number of years the money is invested for.
To calculate A, you need to substitute the values of P, r, n, and t into the formula and perform the necessary calculations.
Here's an example:
Suppose you deposit $1000 into a CD account with an annual interest rate of 4%, compounded annually for 5 years.
P = $1000
r = 0.04
n = 1 (since the interest is compounded annually)
t = 5
The formula becomes:
A = $1000(1 + 0.04/1)^(1*5)
Now, let's evaluate the formula step by step:
1. Divide the annual interest rate by the compound period:
0.04 / 1 = 0.04
2. Add 1 to the result:
1 + 0.04 = 1.04
3. Raise the result to the power of the compound period multiplied by the number of years:
1.04^(1*5) = 1.04^5 ≈ 1.216652
4. Multiply the principal amount by the calculated value:
$1000 * 1.216652 ≈ $1216.65
So, the amount of money returned after 5 years would be approximately $1216.65.
Remember to carry all calculations to 6 decimals, as indicated in the problem, and round the answer to the nearest cent.