let us calculate at what rate of compound interest,rs 10000 amount to rs 11664 in 2 years
Answers
Step-by-step explanation:
Principal = Rs. 10,000
Amount = Rs. 11,664
Time = 2 Years
Rate = ?
\leadsto \sf{Amount = P \times \bigg(1 + \dfrac{r}{100} \bigg)^{t} }⇝Amount=P×(1+100r)t
\leadsto \sf{11664 = 10000 \times \bigg(1 + \dfrac{r}{100} \bigg)^{2} }⇝11664=10000×(1+100r)2
\leadsto \sf{ \dfrac{11664}{10000} = \bigg(1 + \dfrac{r}{100} \bigg)^{2} }⇝1000011664=(1+100r)2
\leadsto \sf{ \sqrt{\dfrac{11664}{10000}}= 1 + \dfrac{r}{100} }⇝1000011664=1+100r
\leadsto \sf{ \sqrt{\dfrac{108 \times 108}{100 \times 100}}= 1 + \dfrac{r}{100} }⇝100×100108×108=1+100r
\leadsto \sf{ \dfrac{108}{100}= 1 + \dfrac{r}{100} }⇝100108=1+100r
\leadsto \sf{ \dfrac{108}{100} - 1= \dfrac{r}{100} }⇝100108−1=100r
\leadsto \sf{ \dfrac{8}{\cancel{100}}= \dfrac{r}{\cancel{100}} }⇝1008=100r
\leadsto \boxed{\sf{r = 8\%}}⇝r=8%
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\therefore∴ At rate 8% p.a. Rs.10,000 will turnRs.11,664 in 2 Years compounded yearly.