In what time will Rs 1000 amount to Rs 1331 at 10% per annum, compounded annually?

To find the time it takes for Rs 1000 to amount to Rs 1331 at 10% per annum, compounded annually, we can use the compound interest formula:

A = P(1 + r/n)^(nt)

Where:
A = the final amount (Rs 1331)
P = the principal amount (Rs 1000)
r = the annual interest rate (10% or 0.10)
n = the number of times interest is compounded per year (in this case, annually)
t = the number of years we are trying to find

We can rearrange this formula to solve for t:

(1 + r/n)^(nt) = A/P

Substituting the given values:

(1 + 0.10/1)^(1*t) = 1331/1000

Simplifying:

(1.10)^t = 1.331

To find t, we need to take the logarithm of both sides of the equation. Since we are looking for the number of years, we can use the natural logarithm (ln):

ln(1.10^t) = ln(1.331)

Using logarithmic properties:

t * ln(1.10) = ln(1.331)

Finally, we can solve for t by dividing both sides by ln(1.10):

t = ln(1.331) / ln(1.10)

Using a calculator, we can find the approximate value of t, which is the number of years it takes for Rs 1000 to amount to Rs 1331 at 10% per annum, compounded annually.

When is

1000(1.10)^n = 1331 ?

1.1^n = 1.331
take log of both sides, and use log rules
n log 1.1 = log 1.331
n = log 1.331/log 1.1
= ....

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