Essentials Of Investments
11th Edition
ISBN: 9781260013924
Author: Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher: Mcgraw-hill Education,
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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.](https://content.bartleby.com/qna-images/question/69da6d7b-7352-4dea-8ba3-a40ad4f9d8c3/5bbcbca3-8264-4e7e-8f1c-cc56c3cc9722/kknhp7s_processed.jpeg)
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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- Lastly, Hector wants to invest in a certificate of deposit (CD) to purchase a boat that costs $28,500 when he retires. Leaf Investments offers a CD with 13% compounded semiannually. How much would Hector have to put in the CD today to gain $28,500 in 30 years?arrow_forwardA couple is planning to finance its three-year-old son's university education. Money can be deposited at 10% compounded quarterly. What quarterly deposit must be made from the son's 3rd birthday to his 18th birthday to provide $8000 on each birthday from the 18th to the 21st? (Note that the first deposit is made three months after the 3rd birthday and the last deposit is made on the date of the first withdrawal.) Answer:arrow_forwardNoah invests $600 at the end of each quarter for 30 years in an account paying 5.64% interest compounded quarterly and then he retires. Suppose that he was in the 15% bracket when the deposits were made and interest was earned. Suppose his tax bracket is now 33% in retirement. Find the current after-tax value of Noah's account if it was set-up as (i) a Traditional Individual Retirement Account (IRA): $ (ii)a Roth Individual Retirement Account (Roth-IRA): $arrow_forward
- 20.arrow_forwardAt the time of her grandsons birth, a grandmother deposits 3000 in an account that pays 6.5% compounded monthly. What will be the value of the account at the child’s 21st birthday, assuming that no other deposits or withdrawals are made during this periodarrow_forwardBeth borrows $7000 on September 20, 2019 at 12% monthly. What will she owe on March 17, 2021?arrow_forward
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