Answer: $3516.26
Explanation:
For this problem, let’s assume that the money was put into the account on the first day of the year. With this in mind, we know that there are four quarters in a year. So, let’s set up a series of expressions to find the annually compounded interest.
Quarter 1: $3100 + ($3100 * .032) = $3199.2
Quarter 2: $3199.2 + ($3199.2 * .032) = $3301.5744
Quarter 3: $3301.5744 + ($3301.5744 * .032) = $3407.22478
Quarter 4: $3407.22477 + ($3407.22477 * .032) = $3516.25596
So, the exact amount would be $3516.25596. The rounded amount would be $3516.26.
We can extract from this series of expressions an equation to solve this faster.
Consider our base principle, P, and the interest, I. And let Q be the periods of interest, in our case quarters. We can say the following:
Returns = P (1 + I)^Q
With this we can calculate the same value as before:
P (1 + I)^Q
= 3100 (1+0.032)^4
= 3100 (1.13427612)
= 3516.25597
= $3516.26
Cheers.
