You deposited $5000 in an investment fund that pays 4.5% per year, compounded quarterly. How much interest will you earn over a period of 5 years?
5000(1 + .045/4)^(4*5) - 5000 = 1253.75
Thank you sooo much for this! It’s correct
To calculate the interest earned over a period of 5 years, we need to use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = the total amount (including both the initial deposit and the interest earned)
P = the principal amount (initial deposit)
r = annual interest rate (as a decimal)
n = number of times the interest is compounded per year
t = number of years
In this case, the principal amount (P) is $5000, the annual interest rate (r) is 4.5% or 0.045 as a decimal, and the interest is compounded quarterly, so the number of times the interest is compounded per year (n) is 4. The time period (t) is 5 years.
Let's calculate the interest earned:
A = 5000(1 + 0.045/4)^(4*5)
A = 5000(1 + 0.01125)^(20)
A = 5000(1.01125)^(20)
A ≈ 5000(1.235) [rounded to 3 decimal places]
A ≈ 6175.82
To find the interest earned, we subtract the initial principal amount from the total amount:
Interest = A - P
Interest = 6175.82 - 5000
Interest ≈ $1175.82
So, you will earn approximately $1175.82 in interest over a period of 5 years.