Question

A Sum of Money Invested at $8\%$ Per Annum For Simple Interest Amounts To$Rs12122$ In $2$ Years. What Will It Amounts To In $2$ Year$8$ Months At $9\%$ Rate Of Interest?

Answer 1

Amount$=Rs12122$

Time period,$t=2years$

Rate of interest,$r=8\%$

$Amount=Principal+Interest$

$$\begin{gathered} 12122=P+\frac{PRT}{100} \\ 12122=\frac{100P+PRT}{100} \\ 12122=\frac{P(100+RT)}{100} \\ 12122=\frac{P(100+8\times 2)}{100} \\ 12122=\frac{116P}{100} \\ P=\frac{12122\times 100}{116} \\ P=10450 \end{gathered}$$

Therefore Principal(P) $=₹10450$

Now amount in two year to eight month $(32months)$ and rate of interest $r=9\%p.a.$ $\frac{8}{3}years$

$$\begin{gathered} A=10450+\frac{10450\times {\displaystyle \frac{8}{3}}\times 9}{100} \\ A=10450+\frac{250800}{100} \\ A=\frac{10450+2508}{} \\ A=12958 \end{gathered}$$

Hence the Amount is $₹12958$