A $2600 investment is made for a three year period at an interest rate of 6.5% per year, compounded annually. How much interest will be earned over the term?
To calculate the interest earned over the three-year period, we need to use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A is the future value of the investment
P is the principal amount (the initial investment)
r is the annual interest rate (in decimal form)
n is the number of compounding periods per year
t is the number of years
In this case, the principal amount (P) is $2600, the annual interest rate (r) is 6.5% or 0.065 (in decimal form), the compounding periods per year (n) is 1 (since it's compounded annually), and the number of years (t) is 3.
Plugging these values into the formula, we can calculate the future value (A):
A = 2600(1 + 0.065/1)^(1*3)
A = 2600(1.065)^3
A ≈ 2600(1.19562825)
A ≈ 3113.62
Now, to calculate the interest earned, we subtract the principal amount from the future value:
Interest = A - P
Interest = 3113.62 - 2600
Interest ≈ 513.62
Therefore, the interest earned over the three-year period will be approximately $513.62.