Calculate the interest earned on an investment of 2500 invested at an interest rate of 6.15%/a compounded quarterly for 10 years.
40 periods at a rate of .0615/4
2500 (1.015375)^40=2500(1.841) = $4602.55
To calculate the interest earned on an investment, we need to use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = the final amount after the investment period
P = the principal amount (or initial investment)
r = the annual interest rate (written as a decimal)
n = the number of times interest is compounded per year
t = the number of years the money is invested for
In this case, the principal amount (P) is $2500, the annual interest rate (r) is 6.15%/a (or 0.0615 written as a decimal), interest is compounded quarterly (so n = 4), and the investment period (t) is 10 years.
To calculate the interest earned, we need to find the difference between the final amount (A) and the principal amount (P). Let's calculate it step by step:
Step 1: Convert the annual interest rate to the quarterly interest rate.
Quarterly interest rate = annual interest rate / number of compounding periods per year = 0.0615 / 4 = 0.015375.
Step 2: Calculate the final amount (A) after 10 years using the formula.
A = P(1 + r/n)^(nt)
A = $2500(1 + 0.015375)^(4*10)
A ≈ $2500(1.015375)^(40)
A ≈ $2500 * 1.783927136
A ≈ $4459.82 (rounded to two decimal places)
Step 3: Calculate the interest earned by subtracting the principal amount (P) from the final amount (A).
Interest earned = A - P
Interest earned = $4459.82 - $2500
Interest earned ≈ $1959.82
Therefore, the interest earned on the investment of $2500, compounded quarterly at an interest rate of 6.15%/a for 10 years, is approximately $1959.82.