Q64. Suppose you deposit a principal ... [FREE SOLUTION]

Chapter 10: Q64. (page 529)

Suppose you deposit a principal amount of P dollars in a bank account that pays compound interest. If the annual interest rate is r (expressed as a decimal) and the bank makes interest payments n times every year, the amount of money A you would have after t years is given by $A (t) = P {(1 + \frac{r}{n})}^{n t}$
Find the account balance after 20 years.

Short Answer

Expert verified

The account balance after 20 years is$2216.72.

Step by step solution

Step 1. Given Information.

Given, if a principal amount of P dollars is deposited in a bank account that pays compound interest and the annual interest rate is r (expressed as a decimal) and the bank makes interest payments n times every year, the amount of money A after t years is given by $A (t) = P {(1 + \frac{r}{n})}^{n t}$

The equation giving the amount of money after t years if $1000 is deposited into an account paying 4% annual interest compounded quarterly (four times per year) is $A (t) = 1000 {(1.01)}^{4 t}$

The account balance after 20 years is to be determined.

Step 2. Explanation.

Since the balance is to be determined after 20 years, $t = 20$

Plugging the values in the equation:

$\begin{array}{l} A (t) = 1000 {(1.01)}^{4 t} \\ A (t) = 1000 {(1.01)}^{4 (20)} \\ A (t) = 1000 {(1.01)}^{80} \\ A (t) = 1000 (2.2167) \\ A (t) 鈮� 2216.72 \end{array}$

Step 3. Conclusion.

Hence the account balance after 20 years is $2216.72

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Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Explanation.

Step 3. Conclusion.

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