How much was the interest of an investment with a future value of $36,920 and interest at 4% compounded monthly for a period of 2.5 years?

To calculate the interest earned on an investment, we first need to find out the initial principal amount. We can do this by using the formula for compound interest which is:

A = P(1 + r/n)^(nt)

Where: A = the future value of the investment/loan, including interest P = the principal investment amount (the initial deposit or loan amount) r = annual interest rate (in decimal) n = number of times that interest is compounded per year t = time the money is invested for in years

Given: A = $36,920 r = 4% or 0.04 (in decimal) n = 12 (as it is compounded monthly) t = 2.5 years

We can rearrange the formula to solve for P:

P = A / (1 + r/n)^(nt)

Substituting the given values:

P = $36,920 / (1 + 0.04/12)^(12*2.5)

Calculate the value inside the bracket first:

= $36,920 / (1 + 0.00333333333)^(30)

Then calculate the exponent:

= $36,920 / 1.103033301

Finally, divide $36,920 by the result above to get the initial principal amount:

P = $36,920 / 1.103033301 =$33,468.75 (approximately)

Now, to find the interest earned, subtract the initial principal from the future value:

Interest = Future Value - Principal Interest = $36,920 -$33,468.75 Interest = $3,451.25

So, the interest of the investment was approximately $3,451.25.