Question

Principal

Time (years)
Rate of compound interest
Compounded
Periods
Rate
Total amount
Total interest
$575
1
4
%
Quarterly
%

Answer 1

To calculate compound interest on $575 for 1 year at an annual rate of 4% compounded quarterly, we use the formula Total future amount = $575 x
`(1 + 0.01)^4`. The total amount is approximately $597.85, and the compound interest is around $22.85.

Step-by-step explanation:

Understanding Compound Interest

Compound interest is an interest rate calculation on the principal plus the accumulated interest over time. It differs from simple interest which is only calculated on the principal amount. To find the compound interest, we use the formula:

Total future amount = Principal x (1 + interest rate)time

For the student's question of calculating the compound interest on a principal of $575 at a rate of 4% compounded quarterly for 1 year, the interest rate per quarter (time period) would be 1% (since 4% annually divided by 4 quarters).

Since it's compounded quarterly, our time will be in quarters (4 quarters per year). The compound interest formula adjusted for quarterly compounding is:

Total future amount = Principal x
`(1 + quarterly interest rate)^(4 * time in years)`

Substituting the given values:

Total future amount = $575 x
`(1 + 0.01)^4`

The final calculation gives us both the total amount and the total interest earned over the compounding periods. Now let's perform the calculations:

Future Value = $575 x
`(1 + 0.01)^4`
= $575 x
`(1.01)^4`
= $575 x 1.04060401
≈ $597.85

Compound interest = Future Value - Present Value
= $597.85 - $575
≈ $22.85

The total amount after 1 year is approximately $597.85, and the total compound interest earned is about $22.85.

Answer 2

In this case, the total amount after 1 year with a 4% compound interest rate and quarterly compounding is $598, and the total interest earned is $23.

Step-by-step explanation:

Compound interest is an interest rate calculation on the principal plus the accumulated interest. To find the compound interest, we determine the difference between the future value and the present value of the principal. This is accomplished by using the formula: Compound Interest = Future Value - Present Value.

In this case, we have a starting principal of $575, a time period of 1 year, a compound interest rate of 4%, and quarterly compounding.

Using the formula, we can calculate the total amount and total interest:

Total Amount = Principal + Compound Interest

Total Interest = Total Amount - Principal

Let's plug in the given values:

Total Amount = $575 + ($575 x 0.04 x 1)

Total Interest = $575 x 0.04 x 1

After finding the values, we have:

Total Amount = $575 + $23 = $598

Total Interest = $23