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Chapter 46: Chapter 46

Problem 1269

Previous question

If $$\$ 100$$ is invested at \(3 \%\) interest compounded annually, how much will it amount to at the end of 18 yrs.?

Short Answer

Expert verified
After investing \(\$100\) at a \(3\%\) annual interest rate compounded annually for 18 years, the final amount will be approximately \(\$170.80\).
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TABLE OF CONTENTS :
TABLE OF CONTENTS

Step 1: Convert the annual interest rate to a decimal

To convert the annual interest rate of 3% to a decimal, we will divide it by 100: \(r = \frac{3}{100} = 0.03\)

Step 2: Substitute the given values into the compound interest formula

Now, we will substitute the given values into the compound interest formula: \(A = P(1 + r/n)^{nt}\) \(A = 100(1 + 0.03/1)^{1 \cdot 18}\)

Step 3: Simplify the expression

Let's simplify the expression: \(A = 100(1 + 0.03)^{18}\) \(A = 100(1.03)^{18}\)

Step 4: Calculate the final amount

Now, we will calculate the final amount by raising 1.03 to the power of 18 and multiplying the result by 100: \(A = 100 \cdot 1.03^{18} \approx 170.80\) So, after 18 years, the initial investment of \(100 will amount to approximately \)170.80.

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