Question

The time by which a sum of money would treble itself at 8% p. a C. I is​

Answer 1

Answer:

The required answer is 14.28 years.

Step-by-step explanation:

Given, Rate of interest = R = 8%

Principal = P

Amount = A = 3P (treble means 3 times of principal)

Time = T in years

By using compound interest formula,

\begin{gathered}A = P(1 + \frac{R}{100})^{T}\\\\= > 3P = P (1+\frac{8}{100})^{T}\\\\= > 3 = (1+0.08)^{T}\\\\= > 3 = (1.08)^{T}\\\\= > ln(1.08)^{T} = ln(3)\\\\= > T ln(1.08) = ln(3) \\\\= > T = \frac{ln(3)}{ln(1.08)}\end{gathered}A=P(1+100R)T=>3P=P(1+1008)T=>3=(1+0.08)T=>3=(1.08)T=>ln(1.08)T=ln(3)=>Tln(1.08)=ln(3)=>T=ln(1.08)ln(3)

=> T = 14.28 years

Hence, the required answer is 14.28 years.