Joe invests $500 into an account earning interest compounded monthly. Determine the rate if there was $625 after 3 years. *Include 2 decimal places in your final answer*
Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
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Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
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![**Problem Statement:**
Joe invests $500 into an account earning interest compounded monthly. Determine the rate if there was $625 after 3 years.
*Include 2 decimal places in your final answer*
**Instructions for Calculation:**
To solve this problem, we can use the formula for compound interest:
\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \]
Where:
- \( A \) is the amount of money accumulated after n years, including interest.
- \( P \) is the principal amount ($500).
- \( r \) is the annual interest rate (in decimal form).
- \( n \) is the number of times interest is compounded per year (12 for monthly).
- \( t \) is the time in years (3 years).
- \( A \) is given as $625.
1. **Substitute the given values into the formula:**
\[ 625 = 500 \left(1 + \frac{r}{12}\right)^{36} \]
2. **Rearrange to solve for \( r \):**
\[ \left(1 + \frac{r}{12}\right)^{36} = \frac{625}{500} \]
3. **Calculate:**
\[ \left(1 + \frac{r}{12}\right)^{36} = 1.25 \]
4. **Apply the 36th root to both sides:**
\[ 1 + \frac{r}{12} = \sqrt[36]{1.25} \]
5. **Solve for \( r \):**
\[ \frac{r}{12} = \sqrt[36]{1.25} - 1 \]
6. **Multiply by 12 to find the annual rate \( r \):**
\[ r = 12 \left(\sqrt[36]{1.25} - 1\right) \]
7. **Calculate the result and round to two decimal places.**
Enter your final answer including 2 decimal places.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F14a4e0ae-41e1-44a6-b924-44f49d1af8ee%2F74885eda-c390-4e78-879e-39d837705c9f%2Fc63zs4_processed.jpeg&w=3840&q=75)
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