Shawnee is putting $3,500 into an account earning 4.85% interest compounded quarterly. She estimates that it will take just over 11 years for this investment to grow to $6,000. Which of the following is a true statement?
4.85/4 = 1.21625 = quarterly percent
11 years = 44 quarters
(1.0121625)^44 = 1.7022
3,500 * 1.7022 = 5957.70 so agree.
I do not see any list of staetements
To determine which of the following statements is true, we first need to calculate the future value of Shawnee's investment. The formula for compound interest is:
Future Value = Principal * (1 + (Rate / n))^(n * time)
Where:
- Principal is the initial amount invested ($3,500)
- Rate is the interest rate per period (4.85%)
- n is the number of compounding periods per year (quarterly compounding means n=4)
- time is the number of years (11)
Using these values, let's calculate the future value of Shawnee's investment:
Future Value = $3,500 * (1 + (0.0485 / 4))^(4 * 11)
Future Value = $3,500 * (1 + 0.012125)^(44)
Future Value ≈ $3,500 * (1.012125)^(44)
Future Value ≈ $3,500 * 1.781181
Calculating this gives us a future value of approximately $6,234.16.
Now, we can compare this calculated future value to the given statement options to determine which one is true.