The Correct Answer and Explanation is:
The correct answer is A) $214.
This problem requires calculating the future value of a deposit using simple interest. The formula helps us determine how much money is earned on an initial investment over a specific period at a given interest rate. The key information provided is the principal amount, which is the initial deposit of $200; the annual interest rate, which is 7 percent; and the time period, which is 1 year. The goal is to find the total amount in the account after the interest is added.
First, we need to calculate the amount of interest Gloria will earn in one year. The formula for simple interest is: Interest = Principal × Rate × Time. Before we can use this formula, we must convert the interest rate from a percentage to a decimal. To do this, we divide the percentage by 100. So, 7% becomes 7 ÷ 100, which equals 0.07. This decimal form is necessary for accurate calculations.
Now, we can plug the values into the interest formula:
Interest = $200 × 0.07 × 1
Multiplying these numbers together, we find that the interest earned is $14. This $14 represents the additional money Gloria’s deposit has generated over the course of the year.
However, the question asks for how much the deposit will be worth at the end of the year, not just the interest earned. To find the total value, we must add the interest earned to the original principal deposit. The calculation is:
Total Value = Principal + Interest
So, we have: Total Value = $200 + $14, which equals $214.
Therefore, at the end of one year, Gloria’s deposit will be worth
214.Whenwecomparethisresulttothegivenmultiplechoiceoptions,itmatchesoptionA.OptionB(214.Whenwecomparethisresulttothegivenmultiplechoiceoptions,itmatchesoptionA.OptionB(140) and D (
1,200)areincorrectduetocalculationerrors,whileoptionC(1,200)areincorrectduetocalculationerrors,whileoptionC(186) would represent a loss, which is not what happens when earning interest.
