The problem asks to calculate the future value and the interest earned on an investment of $3400 for 3 years at an annual interest rate of 8%, compounded quarterly.

1. Problem Description

The problem asks to calculate the future value and the interest earned on an investment of $3400 for 3 years at an annual interest rate of 8%, compounded quarterly.

2. Solution Steps

First, we need to calculate the future value of the investment. The formula for future value $FV$ of an investment $PV$ compounded $n$ times per year for $t$ years at an annual interest rate $r$ is given by:

$FV = PV(1 + \frac{r}{n})^{nt}$

In this case, we have:

$PV = 3400$

$r = 0.08$

$t = 3$

$n = 4$ (compounded quarterly)

Plugging these values into the formula, we get:

$FV = 3400(1 + \frac{0.08}{4})^{4 \cdot 3}$

$FV = 3400(1 + 0.02)^{12}$

$FV = 3400(1.02)^{12}$

$FV = 3400(1.268241795)$

$FV = 4312.022103$

Rounding to the nearest cent, the future value is $4312.

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Next, we need to calculate the interest earned. The interest earned is the difference between the future value and the present value (initial investment):

$Interest = FV - PV$

$Interest = 4312.02 - 3400$

$Interest = 912.02$

Therefore, the interest earned is $912.

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3. Final Answer

Future value: $4312.02

Interest earned: $912.02