We need to calculate the interest earned on an investment of $6100 for 4 years at an annual interest rate of 12%, compounded monthly.

1. Problem Description

We need to calculate the interest earned on an investment of $6100 for 4 years at an annual interest rate of 12%, compounded monthly.

2. Solution Steps

The formula for compound interest is:

$A = P(1 + \frac{r}{n})^{nt}$

Where:

A = the future value of the investment/loan, including interest

P = the principal investment amount (the initial deposit or loan amount)

r = the annual interest rate (as a decimal)

n = the number of times that interest is compounded per year

t = the number of years the money is invested or borrowed for

In this case:

$P = 6100$

$r = 0.12$

$n = 12$

$t = 4$

Plugging these values into the formula:

$A = 6100(1 + \frac{0.12}{12})^{(12)(4)}$

$A = 6100(1 + 0.01)^{48}$

$A = 6100(1.01)^{48}$

$A = 6100(1.612226078)$

$A = 9834.58$

The interest earned is the future value minus the principal:

$Interest = A - P$

$Interest = 9834.58 - 6100$

$Interest = 3734.58$

3. Final Answer

$3734.58