How much would you need to deposit in an account now in order to have $6000 in the account in 5 years? Assume the account earns 5% interest compounded monthly. Question Help: DVideo Submit Question
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.
![### Investment Compounding Question
**Problem Statement:**
How much would you need to deposit in an account now in order to have $6000 in the account in 5 years? Assume the account earns 5% interest compounded monthly.
**Input Box:**
A text box where you can input your answer, denoted by:
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$ ____________
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**Resources:**
There is a "Question Help" section with a link to a video for additional assistance on solving the problem.
**Action Button:**
A blue button labeled "Submit Question" for submitting your answer.
### Explanation for Compounded Interest Calculation
To solve this problem, you would typically 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 (the initial amount of money).
- \(r\) is the annual interest rate (decimal).
- \(n\) is the number of times that interest is compounded per year.
- \(t\) is the time the money is invested for in years.
Given:
- \(A = 6000\)
- \(r = 0.05\)
- \(n = 12\) (monthly compounding)
- \(t = 5\)
You need to calculate \(P\), the principal amount you should deposit now.
Rearrange the formula to solve for \(P\):
\[ P = \frac{A}{\left(1 + \frac{r}{n}\right)^{nt}} \]
Substitute the given values:
\[ P = \frac{6000}{\left(1 + \frac{0.05}{12}\right)^{12 \times 5}} \]
Calculate this to find the initial deposit required.
### Example Video
For a step-by-step solution, refer to the video linked in the "Question Help" section.
*Note: Use a calculator or financial tool for precise computation.*
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