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Chapter 17: Problem 8

You open a 5-year CD for $1,000 that pays 2% interest, compounded annually. What is the value of that CD at the end of the five years?

Short Answer

Expert verified
The value of the 5-year CD at the end of five years will be approximately $1,104.08.

Step by step solution

01

Identify the given information

In this problem, we are given the following information: - Initial deposit, P = $1,000 - Interest rate, r = 2% per year (0.02 as a decimal) - Time, t = 5 years - Compounding frequency, n = 1 (compounded annually)
02

Use the formula for compound interest

To find the value of the CD at the end of 5 years, we will use the formula for compound interest, which is: A = P(1 + r/n)^(nt) where: A = Value of the CD at the end of 5 years P = Initial deposit ($1,000) r = Interest rate (0.02) n = Compounding frequency (1, compounded annually) t = Time (5 years)
03

Plug the values into the compound interest formula

Now, let's plug the given values into the compound interest formula: A = $1,000(1 + 0.02/1)^(1 * 5)
04

Simplify the expression and solve for A

Let's simplify the expression and solve for A: A = $1,000(1 + 0.02)^5 A = $1,000(1.02)^5 Calculating the value of (1.02)^5, we get: A = $1,000 * 1.10408
05

Calculate the final value and present as a rounded value

Now we can calculate the final value of A and round it to a suitable number of decimal places (two decimal places, since we're dealing with dollars and cents): A = $1,104.08 The value of the 5-year CD at the end of five years will be approximately $1,104.08.

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