Per annum

At a certain time, a sum becomes 4 times at the rate of 5% per annum. At what rate of simple interest the same sum becomes 8 times in the same duration

Correct answer:

P₂ =  7.59 %

Step-by-step explanation:

$$\begin{gathered} r_1=4 \\ {r}_2=8 \\ {p}_1=5\%=\frac{5}{100}=\frac{1}{20}=0.05 \\ {r}_1=(1+p_1{)}^t \\ t\ln (1+p_1)=\ln (r_1)=\ln 4\doteq 1.3863 \\ t=\frac{\ln (r_1)}{\ln (1+p_1)}=\frac{\ln 4}{\ln (1+0.05)}\doteq 28.4134 \\ {r}_2=(1+p_2{)}^t \\ {p}_2=r_2^{1/t}-1=8^{1/28.4134}-1\doteq 0.0759 \\ {P}_2=100\cdot p_2=100\cdot 0.0759=7.59\% \end{gathered}$$

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