A company needs $5,600,000 in 8 years in order to expand their factory. How much should the company invest each week if the investment earns a rate of 8% compounded weekly?
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.
![**Problem Statement:**
A company needs $5,600,000 in 8 years in order to expand their factory. How much should the company invest each week if the investment earns a rate of 8% compounded weekly?
**Solution:**
To solve this problem, we need to use the formula for the future value of an annuity due to compound interest:
\[ FV = P \times \left( \frac{(1 + r)^n - 1}{r} \right) \]
Where:
- \( FV \) is the future value of the investment, which is $5,600,000.
- \( P \) is the weekly investment amount.
- \( r \) is the weekly interest rate, which is 8% annually or \( \frac{0.08}{52} \) weekly.
- \( n \) is the total number of investment periods, which is 8 years or \( 8 \times 52 \) weeks.
Our task is to find \( P \). Rearrange the formula to solve for \( P \):
\[ P = \frac{FV \times r}{(1 + r)^n - 1} \]
By substituting the given values into the formula, we can calculate the weekly investment needed.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc40ea460-008a-4bd3-90aa-d601a0d09835%2Fd370b05b-053d-427c-9d45-5a4099e76c79%2Fd6tzyah_processed.jpeg&w=3840&q=75)
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