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 · 2026-11-03T09:53:56-05:00

Identify the principal $P = \$40,000$, time $t = 2$ years, and rate $r = 0.02$.
Apply the compound amount formula $A = P(1 + r)^t$ to find the total amount $A = 40,000 \times (1.02)^2 = \$41,616$.
Subtract the principal from the total amount to find the interest: $CI = 41,616 - 40,000 = \$1,616$.
Final answer: $\boxed{\text{Amount: \$41,616, Interest: \$1,616}}$.

Explanation

Analysis of Given Data

We are given a principal amount of $P = \$40,000$ invested for $t = 2$ years at an annual interest rate of $r = 2\% = 0.02$. The interest is compounded annually, which means the interest is added to the principal at the end of each year. Our goal is to calculate the final total amount and the total compound interest earned over the 2-year period.

Identification of Formulas

The formula for the total amount $A$ after $t$ years with annual compounding is given by:
\[A = P(1 + r)^t\]
Once the amount $A$ is found, the total compound interest $CI$ can be calculated by subtracting the original principal from the total amount:
\[CI = A - P\]

Calculating the Total Amount

Using the formula $A = P(1 + r)^t$, we substitute the given values:
\[A = 40,000(1 + 0.02)^2\]
\[A = 40,000(1.02)^2\]
\[A = 40,000 \times 1.0404\]
\[A = 41,616\]
So, the total amount after 2 years is $\$41,616$.

Calculating the Compound Interest

Now, we calculate the compound interest by subtracting the initial principal from the total amount:
\[CI = A - P\]
\[CI = 41,616 - 40,000\]
\[CI = 1,616\]
The total compound interest earned is $\$1,616$.

Conclusion

In conclusion, after 2 years at an annual interest rate of $2\%$, the total amount accumulated is $\$41,616$ and the compound interest earned is $\$1,616$. $\boxed{\text{Amount: \$41,616, Interest: \$1,616}}$

Examples

Compound interest is a fundamental concept in finance, crucial for understanding savings accounts, loans, and investments. For example, if you deposit $\$40,000$ in a savings account with a $2\%$ interest rate compounded annually, the bank calculates interest on the original amount plus any interest earned previously. After two years, your money grows to $\$41,616$, effectively earning $\$1,616$ simply by keeping the money in the account. This principle explains how long-term savings grow exponentially over time.