Calculate the amount of interest earned in 10 years on $1000.00 invested at 3.00% per annum, compounded monthly.
1000(1+.03/12)^(12*10) - 1000
To calculate the amount of interest earned on an investment, we need to use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment
P = the principal amount (initial investment)
r = the annual interest rate (expressed as a decimal)
n = the number of times interest is compounded per year
t = the number of years
In this case, the principal amount (P) is $1000.00, the annual interest rate (r) is 3.00% (or 0.03 as a decimal), the number of times compounded (n) is 12 (since it's compounded monthly), and the number of years (t) is 10.
Plugging these values into the formula, we get:
A = 1000(1 + 0.03/12)^(12*10)
Let's break down the calculation step by step:
1. Calculate the exponent inside the parentheses: (12 * 10) = 120.
2. Divide the annual interest rate (0.03) by the number of times compounded per year (12): 0.03/12 = 0.0025.
3. Add 1 to the value obtained in step 2: 1 + 0.0025 = 1.0025.
4. Raise the value obtained in step 3 to the power of the exponent from step 1: 1.0025^120.
Now, using a calculator or spreadsheet, calculate 1.0025 raised to the power of 120:
1.0025^120 ≈ 1.3400963.
Finally, multiply the principal amount (P) by the future value (A) to find the interest earned:
Interest earned = A - P
= 1.3400963 * $1000.00 - $1000.00
≈ $340.10.
Therefore, the amount of interest earned in 10 years on $1000.00 invested at 3.00% per annum, compounded monthly, is approximately $340.10.