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Chapter 5: Q.33 (page 324)

What rate of interest compounded annually is required to triple an investment in 5 years?

Short Answer

Expert verified

The annual rate of interest required to triple the principal in 5 years is 24.57%

Step by step solution

01

Step 1. Given Information

Given certain amount is tripled after 5 years by compounding annually. The rate of interest at which the amount is compounded is to be determined.

02

Step 2. Calculation

According to the compound interest formula, the amount A after t years for the principal P with an annual rate of interest r compounded n times per year is $A = P {(1 + \frac{r}{n})}^{n t}$

Here let the principal be P.

Since the amount is tripled, $A = 3 P$

Since the amount is tripled after 5 years, $t = 5$

And since the interest is compounded annually, $n = 1$

Plugging the values to determine r:

$A = P {(1 + \frac{r}{n})}^{n t} 3 P = P {(1 + \frac{r}{1})}^{(1) (5)} {(1 + r)}^{5} = 3 1 + r = \sqrt[5]{3} 1 + r = 1.24573 . . . r = 1.24573 . . . - 1 r = 0.24573 . . .$

So the rate of interest in decimal form is 0.24573...

Therefore the interest rate is 24.57% (approximately)

03

Step 3. Conclusion

The annual rate of interest required to triple the principal in 5 years is 24.57%

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Most popular questions from this chapter

Answers are given at the end of these exercises. If you get a wrong answer, read the pages listed in red.

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