3. Jay just graduated from college and he has decided to open a retirement account that pays 1.75% interest compounded monthly. If he has direct deposits of $100 per month taken out of his paycheck, how much will he have in the account after 42 years?
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:**
Jay just graduated from college and he has decided to open a retirement account that pays 1.75% interest compounded monthly. If he has direct deposits of $100 per month taken out of his paycheck, how much will he have in the account after 42 years?
**Solution:**
This problem involves calculating the future value of an annuity with compound interest. To solve it, we use the future value of an annuity formula:
\[ FV = P \times \left( \frac{(1 + r)^n - 1}{r} \right) \]
Where:
- \( P \) is the monthly deposit ($100 in this case).
- \( r \) is the monthly interest rate (annual rate divided by 12). For 1.75% annual interest, the monthly rate is \( \frac{0.0175}{12} \).
- \( n \) is the total number of deposits (monthly deposits for 42 years, so \( 42 \times 12 \)).
Let’s break down the numbers:
1. Monthly interest rate \( r = \frac{0.0175}{12} \approx 0.001458 \).
2. Total number of deposits \( n = 42 \times 12 = 504 \).
Using the future value of an annuity formula:
\[ FV = 100 \times \left( \frac{(1 + 0.001458)^{504} - 1}{0.001458} \right) \]
To find the value at term, you can use a calculator or a spreadsheet to perform the calculations.
This transcribed problem is typically found in personal finance or mathematics courses covering compound interest and annuities. Through this scenario, students can learn to apply mathematical formulas to real-life financial planning situations.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0868cb34-caa6-4ad3-96bc-ad3647641b9e%2F77104aaf-6527-47a3-b8c1-ee90bb78ff8b%2Fku61zw_processed.jpeg&w=3840&q=75)
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