Deborah deposits $200 into an account that pays simple interest at the rate of 7%. How much will she have at the end of 4 months?
a) Present Value with simple interest
b) Future Value with simple interest
c) Future Value with compound interest
d) Simple Interest
e) Effective Rate
see whether you can apply these formulas, which you should have seen:
200(1+.07 * 4/12)
200(1+.07)^(4/12)
To find the amount Deborah will have at the end of 4 months with simple interest, we need to calculate the future value.
b) Future Value with simple interest:
The formula to calculate the future value with simple interest is:
Future Value = Present Value + (Present Value * Interest Rate * Time)
Given:
Present Value (P) = $200
Interest Rate (r) = 7% = 0.07 (as a decimal)
Time (t) = 4 months
Plugging these values into the formula:
Future Value = 200 + (200 * 0.07 * 4)
= 200 + (200 * 0.28)
= 200 + 56
= $256
Therefore, Deborah will have $256 at the end of 4 months.
To calculate how much Deborah will have at the end of 4 months, we can use the formula for future value with simple interest:
Future Value = Present Value + (Present Value * Interest Rate * Time)
Here, "Present Value" is the initial deposit, "Interest Rate" is the rate of interest, and "Time" is the time period in years.
Given that Deborah deposits $200 and the interest rate is 7%, we need to convert the time period to years. Since 4 months is 4/12 or 1/3 of a year, our equation becomes:
Future Value = $200 + ($200 * 0.07 * 1/3)
Simplifying the equation:
Future Value = $200 + ($14 * 1/3)
= $200 + $4.67
= $204.67
Therefore, Deborah will have $204.67 at the end of 4 months.
The correct answer is b) Future Value with simple interest.