[2nd year] In which year will the amount on a sum of Rs. 800 at 20% compounded half-yearly exceeds Rs.1000?

In which year will the amount on a sum of Rs. 800 at 20% compounded half-yearly exceeds Rs.1000?

1st year

2nd year

4th year

5th year

Explanation:

Let the time taken for this amount to reach Rs.1000 be X.

The important thing to note is that this sum is compounded half-yearly. Hence, we use the formula:

A = P 1 + [$\dfrac{r}{m*100}]^{mT}$

Where, A= Amount,

P = Principal

r = interest rate

m = no. of periods within a year

T = no. of years

We need to obtain T such that the RHS should be greater than the LHS:

⇒A < P$ (1 + [\dfrac{r}{m*100}]^{mT}$

In this case,

A = 1000

P = 800

r = 20%

m = 2 (since it is half-yearly)

Substituting these values, we have

$1000<800(1+20 / [2*100])^{2T}=800(11/10)^{2T}$

$1000/800<(121/100)^T $

⇒ 1.25 < (1.21)T

Now, we need to use trial and error to check for the values of T.

For T = 1, 1.25 > 1.21, hence the condition is not satisfied.

For T = 2, 1.25 < 1.4641, hence the condition is met.

Therefore, it is the second year in which the amount would be greater than Rs.1000.

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