**Problem 19: Early Withdrawal from a Certificate of Deposit (CD)**Diana invested $8,000 in a 10-year Certificate of Deposit (CD) that offered an annual interest rate of 5%, compounded monthly. After 2 years, Diana decided to withdraw all of her money. Due to an early withdrawal penalty, she had to pay back all the interest she earned during the first year. We need to calculate how much money Diana was left with after these conditions.**Concepts Involved:**- Compound Interest- Early Withdrawal Penalty**Steps to Solve:**1. **Calculate the amount accumulated in the CD after 2 years with monthly compounding:** The formula for compound interest is: \[ A = P \left(1 + \frac{r}{n}\right)^{nt} \] where: - $ A $ is the amount of money accumulated after n years, including interest. - $ P $ is the principal amount (the initial amount of money). - $ r $ is the annual interest rate (decimal). - $ n $ is the number of times that interest is compounded per year. - $ t $ is the time the money is invested for in years. Given: - $ P = $8,000 $ - $ r = 0.05 $ - $ n = 12 $ (monthly compounding) - $ t = 2 $ years Substituting these values into the formula: \[ A = 8000 \left(1 + \frac{0.05}{12}\right)^{12 \times 2} \]2. **Calculate the amount of interest earned after 2 years:** - First, find the value of $ A $: \[ A = 8000 \left(1 + 0.0041667\right)^{24} \approx 8000 \left(1.10494\right) \approx 8839.52 \]3. **Calculate the amount accumulated in the CD after 1 year to determine the interest that must be paid back due to the early withdrawal penalty:** Given: - $ P = $8,000 $ - $ r = 0.05 $ - \( n =

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19. Diana put $8000 in a 10-year CD paying 5% interest compounded monthly. After 2 years, she withdrew all her money, and as an early withdrawal penalty, she paid back all the interest she made during the first year. How much money was Diana left with?

19. Diana put $8000 in a 10-year CD paying 5% interest compounded monthly. After 2 years, she withdrew all her money, and as an early withdrawal penalty, she paid back all the interest she made during the first year. How much money was Diana left with?

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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