Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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![**Compound Interest Calculation Example**
**Scenario:**
At the time of her grandson's birth, a grandmother deposits $2000 in an account that pays 8.5% compounded monthly. What will be the value of the account at the child's twenty-first birthday, assuming that no other deposits or withdrawals are made during this period?
**Calculation:**
The value of the account will be $____.
(Round to the nearest dollar as needed.)
**Discussion:**
This exercise is an application of compound interest, where interest earned is added to the principal, so that the interest of the subsequent period is computed over the principal plus previously accrued interest. In this case, the interest is compounded monthly, which means it is calculated 12 times a year.
To learn how to solve this, use the compound interest formula:
\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \]
Where:
- \( A \) is the amount of money accumulated after n years, including interest.
- \( P \) is the principal amount ($2000).
- \( r \) is the annual interest rate (8.5% or 0.085).
- \( n \) is the number of times that interest is compounded per year (12 for monthly).
- \( t \) is the time the money is invested for in years (21 years).
The required calculation involves substituting these values into the formula, which will yield the final account balance at the grandson's 21st birthday.](https://content.bartleby.com/qna-images/question/58fa9ca8-a7e7-4ecd-98e6-0e2121b1f6b9/3e9f910f-cd6c-488d-8dd7-3ad40e4ef475/gi5d9y2_processed.jpeg)
Transcribed Image Text:**Compound Interest Calculation Example**
**Scenario:**
At the time of her grandson's birth, a grandmother deposits $2000 in an account that pays 8.5% compounded monthly. What will be the value of the account at the child's twenty-first birthday, assuming that no other deposits or withdrawals are made during this period?
**Calculation:**
The value of the account will be $____.
(Round to the nearest dollar as needed.)
**Discussion:**
This exercise is an application of compound interest, where interest earned is added to the principal, so that the interest of the subsequent period is computed over the principal plus previously accrued interest. In this case, the interest is compounded monthly, which means it is calculated 12 times a year.
To learn how to solve this, use the compound interest formula:
\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \]
Where:
- \( A \) is the amount of money accumulated after n years, including interest.
- \( P \) is the principal amount ($2000).
- \( r \) is the annual interest rate (8.5% or 0.085).
- \( n \) is the number of times that interest is compounded per year (12 for monthly).
- \( t \) is the time the money is invested for in years (21 years).
The required calculation involves substituting these values into the formula, which will yield the final account balance at the grandson's 21st birthday.
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