4. On Jacob's first birthday, his grandparents present him with a $5000 certificate of deposit (CD) that earns 2.4% interest, conmpounded quarterly. If the CD matures on his sixteenth birthday, what amount will be available then?
4. On Jacob's first birthday, his grandparents present him with a $5000 certificate of deposit (CD) that earns 2.4% interest, conmpounded quarterly. If the CD matures on his sixteenth birthday, what amount will be available then?
Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Chapter1: Investments: Background And Issues
Section: Chapter Questions
Problem 1PS
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![**Problem 4: Calculating the Maturity Amount of a Certificate of Deposit (CD)**
On Jacob’s first birthday, his grandparents present him with a $5000 certificate of deposit (CD) that earns 2.4% interest, compounded quarterly. If the CD matures on his sixteenth birthday, what amount will be available then?
**Solution Approach:**
To solve this problem, you can use the formula for compound interest:
\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \]
Where:
- \( A \) is the amount of money accumulated after n years, including interest.
- \( P \) is the principal amount ($5000 in this case).
- \( r \) is the annual interest rate (2.4% or 0.024 as a decimal).
- \( n \) is the number of times that interest is compounded per year (quarterly compounding means \( n = 4 \)).
- \( t \) is the time the money is invested for in years (15 years, in this case, from age 1 to age 16).
Plug in the given values to calculate the maturity amount.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F69da6d7b-7352-4dea-8ba3-a40ad4f9d8c3%2F5bbcbca3-8264-4e7e-8f1c-cc56c3cc9722%2Fkknhp7s_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem 4: Calculating the Maturity Amount of a Certificate of Deposit (CD)**
On Jacob’s first birthday, his grandparents present him with a $5000 certificate of deposit (CD) that earns 2.4% interest, compounded quarterly. If the CD matures on his sixteenth birthday, what amount will be available then?
**Solution Approach:**
To solve this problem, you can use the formula for compound interest:
\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \]
Where:
- \( A \) is the amount of money accumulated after n years, including interest.
- \( P \) is the principal amount ($5000 in this case).
- \( r \) is the annual interest rate (2.4% or 0.024 as a decimal).
- \( n \) is the number of times that interest is compounded per year (quarterly compounding means \( n = 4 \)).
- \( t \) is the time the money is invested for in years (15 years, in this case, from age 1 to age 16).
Plug in the given values to calculate the maturity amount.
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