Practice Question
An account was opened with $1,000 ten years ago. Today, the account balance is $1,500. If the account paid interest compounded annually, how much interest on interest was earned?
A) $86.20 B) $93.10 C) $102.39 D) $130.28 E) None of the above
Step 1: Identify Key Variables
- Initial principal \( P = 1,000 \)
- Final balance \( A = 1,500 \)
- Number of years \( n = 10 \)
Step 2: Use Compound Interest Formula
\[ A = P(1 + r)^n \] \[ 1500 = 1000(1 + r)^{10} \Rightarrow (1 + r)^{10} = 1.5 \Rightarrow 1 + r = 1.5^{1/10} \approx 1.0414 \Rightarrow r \approx 0.0414 \text{ or } 4.14\% \]
Step 3: Total Interest Earned
\[ \text{Total Interest} = A - P = 1500 - 1000 = 500 \]
Step 4: Calculate Simple Interest
\[ \text{Simple Interest} = P \times r \times n = 1000 \times 0.0414 \times 10 = 414 \]
Step 5: Interest on Interest
\[ \text{Interest on Interest} = \text{Total Interest} - \text{Simple Interest} = 500 - 414 = 86 \]
Conclusion:
The interest earned on reinvested interest is approximately $86.20, corresponding to option A.