Find the amount and compound interest on $40,000 for 2 years at 2% per annum.

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03-11-2026
Mathematics

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Find the amount and compound interest on $40,000 for 2 years at 2% per annum.

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GinnyAnswer GinnyAnswer · Answer 1 · 2026-11-03T09:54:30-05:00

Identify the principal $P = \$40,000$, annual interest rate $r = 0.02$, and time $n = 2$ years.
Calculate the total amount using the formula $A = P(1+r)^n$: $A = 40,000(1.02)^2 = \$41,616$.
Calculate the compound interest by finding the difference between the amount and principal: $CI = 41,616 - 40,000 = \$1,616$.
The final results are: Total Amount = $\boxed{\$41,616}$, Compound Interest = $\boxed{\$1,616}$.

Explanation

Analysis of the Problem

We are tasked with calculating the final amount and the compound interest for an initial principal of $\$40,000$ invested over $2$ years at an annual interest rate of $2\%$, compounded annually. Here, the principal $P = 40,000$, the annual interest rate $r = 2\% = 0.02$, and the time $n = 2$ years.

Calculating the Total Amount

The formula for the total amount $A$ after $n$ years with annual compounding is:
\[A = P(1 + r)^n\]
Substituting our known values:
\[A = 40,000(1 + 0.02)^2 = 40,000(1.02)^2\]
First, we calculate $1.02^2$:
\[1.02 \times 1.02 = 1.0404\]
Then, we find the total amount:
\[A = 40,000 \times 1.0404 = 41,616\]
So, the total amount after $2$ years is $\$41,616$.

Calculating the Compound Interest

The compound interest $CI$ is the difference between the total amount $A$ and the original principal $P$:
\[CI = A - P\]
Substituting the values:
\[CI = 41,616 - 40,000 = 1,616\]
Therefore, the compound interest earned after $2$ years is $\$1,616$.

Examples

Compound interest is a fundamental concept in finance used to understand how savings grow over time. For example, if you deposit money into a savings account that pays compound interest, your earnings each year are added to the principal, meaning that in the following year, you earn interest on both your original deposit and the interest you already earned. This "interest on interest" effect can significantly increase the total return on your investments over long periods, demonstrating the power of time in wealth accumulation.