A bank features a savings account that has an annual percentage rate of r = 2.9% with interest compounded semi-annually. Chris deposits $4,000 into the account. The account balance can be modeled by the exponential formula S(t) = P(1 + )", nt where S is the future value, P is the present value, r is the annual percentage rate, n is the number of times each year that the interest is compounded, and t is the time in years. (A) What values should be used for P, r, and n? P = r = n = (B) How much money will Chris have in the account in 9 years? Answer = $ Round answer to the nearest ny. = (C) What is the annual percentage yield (APY) for the savings account? (The APY is the actual or effective annual percentage rate which includes all compounding in the year). APY= Round answer to 3 decimal places.
A bank features a savings account that has an annual percentage rate of r = 2.9% with interest compounded semi-annually. Chris deposits $4,000 into the account. The account balance can be modeled by the exponential formula S(t) = P(1 + )", nt where S is the future value, P is the present value, r is the annual percentage rate, n is the number of times each year that the interest is compounded, and t is the time in years. (A) What values should be used for P, r, and n? P = r = n = (B) How much money will Chris have in the account in 9 years? Answer = $ Round answer to the nearest ny. = (C) What is the annual percentage yield (APY) for the savings account? (The APY is the actual or effective annual percentage rate which includes all compounding in the year). APY= Round answer to 3 decimal places.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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![**Exponential Growth in a Savings Account**
A bank offers a savings account with an annual percentage rate \( r = 2.9\% \) with interest compounded semi-annually. Chris deposits $4,000 into this account.
The account balance can be modeled by the exponential formula:
\[
S(t) = P \left(1 + \frac{r}{n}\right)^{nt}
\]
Where:
- \( S \) is the future value.
- \( P \) is the present value.
- \( r \) is the annual percentage rate.
- \( n \) is the number of times each year that the interest is compounded.
- \( t \) is the time in years.
**(A) What values should be used for \( P \), \( r \), and \( n \)?**
\[ P = \_\_\_\_ , \quad r = \_\_\_\_ , \quad n = \_\_\_\_ \]
**(B) How much money will Chris have in the account in 9 years?**
Answer = \$\_\_\_\_
*Round answer to the nearest penny.*
**(C) What is the annual percentage yield (APY) for the savings account?**
(The APY is the actual or effective annual percentage rate which includes all compounding in the year.)
APY = \_\_\_\_%
*Round answer to 3 decimal places.*](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3e8ca5a6-77b3-4f88-a5f3-282372d2c0e0%2Fc899d7be-835b-47e1-993b-3571e0783b6b%2Fzl637rk_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Exponential Growth in a Savings Account**
A bank offers a savings account with an annual percentage rate \( r = 2.9\% \) with interest compounded semi-annually. Chris deposits $4,000 into this account.
The account balance can be modeled by the exponential formula:
\[
S(t) = P \left(1 + \frac{r}{n}\right)^{nt}
\]
Where:
- \( S \) is the future value.
- \( P \) is the present value.
- \( r \) is the annual percentage rate.
- \( n \) is the number of times each year that the interest is compounded.
- \( t \) is the time in years.
**(A) What values should be used for \( P \), \( r \), and \( n \)?**
\[ P = \_\_\_\_ , \quad r = \_\_\_\_ , \quad n = \_\_\_\_ \]
**(B) How much money will Chris have in the account in 9 years?**
Answer = \$\_\_\_\_
*Round answer to the nearest penny.*
**(C) What is the annual percentage yield (APY) for the savings account?**
(The APY is the actual or effective annual percentage rate which includes all compounding in the year.)
APY = \_\_\_\_%
*Round answer to 3 decimal places.*
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