Question

you want to deposit $4,000 in a bank where you earn an interest rate of 6 percent per year. what will its future value be after five years?
p =

i = % =

t =

future value = p × (1 + i)^t
= 4,000 × (1 + 0.06)^5
=

the future value of $4,000 after five years is $ .
summary
how are the formulas for future and present value related?

Explanation:

Step1: Identify the principal amount (P)

The principal amount \( P \) is the initial deposit, which is $4,000. So \( P = 4000 \).

Step2: Identify the interest rate (i)

The annual interest rate is 6 percent. To convert a percentage to a decimal, we divide by 100. So \( i = 6\% = \frac{6}{100} = 0.06 \).

Step3: Identify the time period (t)

The time period \( t \) is 5 years. So \( t = 5 \).

Step4: Calculate the future value

Using the future - value formula \( \text{future value}=P\times(1 + i)^{t} \), substitute \( P = 4000 \), \( i=0.06 \), and \( t = 5 \) into the formula:
\[

$$\begin{align*} \text{future value}&=4000\times(1 + 0.06)^{5}\\ &=4000\times1.06^{5}\\ &=4000\times1.3382255776\\ &=5352.9023104 \end{align*}$$

\]

Answer:

• \( P=\boldsymbol{4000} \)
• \( i = \boldsymbol{6}\%=\boldsymbol{0.06} \)
• \( t=\boldsymbol{5} \)
• \( 4000\times(1 + 0.06)^{5}=\boldsymbol{5352.90} \) (rounded to two decimal places)
• The future value of $4,000 after five years is \(\boldsymbol{\$5352.90}\)