Question

In how many years will rs 3375 become rs 4096 at 13 1/3 percentage p.a where interest is compounded half_yearly​

Answer 1

Answer:

Principal, P = Rs. 3375

Amount, A = Rs. 4096

Since it is compounded on a half-yearly basis, so,

Let the time period be “n” half years.

And the rate of interest, R = R/2 = ½ * 13$\frac{1}{3}$ = $\frac{20}{3}$ %.

The formula for calculating the amount in compound interest is given as,

A = P [1+ R/100]ⁿ

Substituting the given values, we get

4096 = 3375 [1+ (20/300)]ⁿ

⇒ 4096/3375 = [1 + 2/30]ⁿ

⇒ 1.21 = [32/30]ⁿ

Taking log on both sides

⇒ log 1.21 = log (1.06)ⁿ

⇒ log 1.21 = n log 1.06 ….. [since log aᵇ = b log a]  

⇒ 0.0827 = n * 0.0253

⇒ n = 0.0827/0.0253

⇒ n = 3.2 ≈ 3 half years

We got n = 3 half years, therefore the required time period will be = 3/2 years = 1.5 years

Thus, in 1.5 years rs 3375 become rs 4096 at 13 1/3 percentage p.a. where the interest is compounded half-yearly.