   Chapter 2.2, Problem 87E

Chapter
Section
Textbook Problem

Investments Refer to Exercise 85. In August of which year will an investment of$5,000 made in August 2013 first exceed$5,050? [HINT: See Example 5; you saw this exercise before in Section 1.2.]

To determine

To calculate: The time when investment of $5000 exceeds$5050 if E*TRADE Financial was giving 0.05% interest on online checking accounts reinvested monthly.

Explanation

Given Information:

E*TRADE Financial was giving 0.05% interest on online checking accounts reinvested monthly and the amount of $5000 deposited in August 2014. The new worth of amount is$5050

Formula used:

The formula for compound interest is,

A(t)=P(1+rm)mt

Here, P is initial amount, m is the number of times interest is reinvested in a year, r is rate of interest and t is time in year.

Calculation:

Convert the rate of interest in the decimal form.

r=0.05%=0.05100=0.0005

Since the interest is reinvested monthly therefore the value of m is,

m=12

Consider the formula of compound interest is,

A(t)=P(1+rm)mt

Substitute P=$5000, r=0.0005 and m=12 in the expression A(t)=P(1+rm)mt. A(t)=$5000(1+0

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