Need help setting up the problem: If you deposited $800 into a savings account with an interest rate of 3.8%, what will be your balance at the end of 1 year. I was thinking the overall answer is 830.40 but you are supposed to use a percent equation and a proportion equation. I don't know how to do that in this situation. Thanks..
Compounded Annually:
P = Po(1+r)^n.
n = 1Comp/yr * 1yr = 1.
P = 800(1.038)^1 = $830.40
Simple Int.
P = P + Po*r*t = 800 + 800*0.038*1= $830.40.
To calculate the balance at the end of 1 year, you can use the formula for simple interest:
Interest = Principal * Rate * Time
Where:
Principal = $800 (initial deposit)
Rate = 3.8% (expressed as a decimal, so 3.8/100 = 0.038)
Time = 1 year
Step 1: Calculate the interest earned:
Interest = 800 * 0.038 * 1
Interest = $30.40
Step 2: Add the interest earned to the initial deposit:
Final balance = Deposit + Interest
Final balance = $800 + $30.40
Final balance = $830.40
So, your intuition was correct. The balance at the end of 1 year will be $830.40.
If you would like me to explain how to solve this using a percent equation and a proportion equation, please let me know.
To solve this problem using both a percent equation and a proportion equation, we first need to understand the concepts behind each equation.
1. Percent equation: A percent equation expresses the relationship between a part and a whole using a percentage. It can be represented as follows:
Part = (Percentage / 100) × Whole
In this case, the "part" is the interest earned on the deposit, the "percentage" is the interest rate of 3.8%, and the "whole" is the initial deposit of $800. By applying this equation, we can calculate the interest earned.
2. Proportion equation: A proportion equation represents an equivalence between two ratios or fractions. It can be expressed as follows:
(Part/Whole) = (Part/Whole)
In this case, the "part" is the interest earned on the deposit, and the "whole" is the initial deposit plus the interest earned. By setting up a proportion equation, we can determine the new balance.
Now let's solve the problem step by step:
Step 1: Calculate the interest earned using the percent equation.
Part = (3.8 / 100) × 800
Part = 0.038 × 800
Part = 30.4
Step 2: Calculate the new balance using the proportion equation.
(Part/Whole) = (Part/Whole)
(30.4 / (800 + 30.4)) = (30.4 / Whole)
Cross-multiplying, we get:
30.4 × Whole = (800 + 30.4) × 30.4
Simplifying the equation:
30.4 × Whole = 24320 + 924.16
30.4 × Whole ≈ 25244.16
Solving for Whole:
Whole ≈ 25244.16 / 30.4
Whole ≈ 829.473
So, the approximate balance at the end of 1 year will be $829.47 (rounded to the nearest cent).
It's important to note that using the percent equation and proportion equation helps to understand and solve the problem step by step, ensuring accuracy in the calculations.