Question

In what time will 1500 yield 496.50 as compound interest at 10% per annum compounded annually .

Answer 1

Given:

1500 yields 496.50 as compound interest at 10% per annum compounded annually.

To find:

The time period

Solution:

To solve the given problem we will use the following formula:

$\boxed{\bold{C.I. = P [(1 + \frac{R}{100})^n - 1]}}$

where

P = principal

R = rate of interest

n = time period

Now, we will substitute C.I. = Rs. 496.50, P = Rs. 1500 and R = 10% in the above formula:

$496.50 = 1500[(1+ \frac{10}{100})^n - 1]$

$\implies \frac{496.50}{1500} = [(1+ \frac{10}{100})^n - 1]$

$\implies \frac{49650}{150000} = [( \frac{110}{100})^n - 1]$

$\implies 0.331 = [( \frac{110}{100})^n - 1]$

$\implies 0.331 + 1 = ( \frac{11}{10})^n$

$\implies 1.331 = ( \frac{11}{10})^n$

$\implies \frac{1331}{1000} = ( \frac{11}{10})^n$

$\implies (\frac{11}{10})^3 = ( \frac{11}{10})^n$

$\implies \bold{n = 3 \:years}$

Thus, in 3 years Rs. 1500 will yield Rs. 496.50 as compound interest at 10% p.a. compounded annually.

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Answer 2

Answer:

There You Go

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