Question

An investment of $6,000 was placed for 3 years at 4.25% compounded annually. How much more would be collected if the investment was compounded quarterly? The amount compounded annually was [insert amount], and the amount compounded quarterly was [insert amount].

Answer 1

To find the difference in amounts collected with annual vs. quarterly compounding on a $6,000 investment, we use the compound interest formula. The investment compounded quarterly garners $33.70 more over three years than if it were compounded annually.

Step-by-step explanation:

The question we are addressing is a mathematics problem, specifically one involving compound interest and how it is affected by different compounding periods. When investments are compounded more frequently, they generally accumulate more interest. Using the formulas for compound interest, we can calculate the future value of the $6,000 investment compounded annually and quarterly.

For annual compounding at 4.25% for 3 years, the formula A =
`P(1 + r/n)^((nt) )`gives us: A = $
`6,000(1 + 0.0425/1)^((1*3))` = $6,819.09 approximately.

For quarterly compounding, the formula is modified to account for the frequency, rendering A =
`P(1 + r/n)^((nt))` into: A = $
`6,000(1 + 0.0425/4)^((4*3))` = $6,852.79 approximately.

The difference collected with quarterly compounding compared to annual compounding is $6,852.79 - $6,819.09 = $33.70.