Question

In how many years will ₹ 3375 becomes ₹ 4096 at 13 1/3% p.a where interest is compound half yearly​

Answer 1

Answer:

One year is the time period.

Step-by-step explanation:

Principle money= Rs 3375

Amount = Rs 4096

Rate of interest= 13(1/3) =40/3%

Let time = T.

Now,

4096 = 3375(1+(40/3) /2×100) ^(2T)

(1+(20/3) /100) ^(2T)= (4096/3375)

(32/30)^(2T) =1.21

1.1^(2T) = 1.21

1.1^T=√1.21

1.1^T= 1.1

Comparing both sides, we can say,

T= 1.

Therefore time is one year.

Answer 2

Step-by-step explanation:

Given  

In how many years will ₹ 3375 becomes ₹ 4096 at 13 1/3% p.a where interest is compound half yearly

Principal P = Rs 3375

Amount A = Rs 4096

Since it is compounded on half yearly time period = n

Rate of interest R = R/2 = 40/3 x 1/2 = 20 / 3

We know that

A = P(1 + R/100 )^n

4096 = 3375 (1 + (20/300)^n

4096 / 3375 = (32 / 30)^n

1.21 = (1.06)^n

Log 1.21 = n log 1.06

0.0827 = n x 0.0253

So n = 3.2 or 3 + 0.2(3 half years)

             = 1/2 + 1/2 + 1/2  

             = 1.5 years