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.

ENGR.ECONOMIC ANALYSIS
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ISBN:9780190931919
Author:NEWNAN
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Chapter1: Making Economics Decisions
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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.*
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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