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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 isA=P1+rnnt

Here let the principal be P.

Since the amount is tripled,A=3P

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=P1+rnnt3P=P1+r1151+r5=31+r=351+r=1.24573...r=1.24573...-1r=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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