Harold invested a certain amount of money in an account earning 5.5% interest compounded TWICE a month. After 10 years, there was $9050 in the account. How much did he originally invest?
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
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
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
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
![### Compound Interest Calculation Exercise
**Problem Statement:**
Harold invested a certain amount of money in an account earning 5.5% interest compounded **twice a month**. After 10 years, there was $9050 in the account. How much did he originally invest?
**Formula for Compound Interest:**
\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \]
- \( A \) = the amount of money accumulated after n years, including interest.
- \( P \) = the principal amount (the initial amount of money)
- \( r \) = annual interest rate (decimal)
- \( n \) = number of times that interest is compounded per year
- \( t \) = the number of years the money is invested for
**Given Data:**
- Final Amount (\( A \)) = $9050
- Annual Interest Rate (\( r \)) = 5.5% or 0.055
- Compounding Frequency (\( n \)) = twice a month = 24 times a year
- Time (\( t \)) = 10 years
**To Find:**
- The original investment (\( P \))
**Solution:**
We need to rearrange the compound interest formula to solve for \( P \):
\[ P = \frac{A}{\left(1 + \frac{r}{n}\right)^{nt}} \]
**Inserting the Values:**
\[ P = \frac{9050}{\left(1 + \frac{0.055}{24}\right)^{24 \times 10}} \]
**Calculate \( P \) and Round Answer to 2 Decimal Places:**
\[ \text{The original investment was } \$ \boxed{\text{ \_\_\_\_\_ }} \text{. Round answer to 2 decimal places} \]
**Interactive Calculation:**
Use the formula above and a calculator to find the precise value for \( P \).
This exercise helps students understand the concept of compound interest and how it is applied in financial scenarios.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F54e8c682-be67-4ef0-bd1d-cf8b2e543b76%2Fe4e1a3c4-e1f5-4a88-9de2-1236a5fc8132%2Fg4lkjuq_processed.png&w=3840&q=75)
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