Question

simple interest on a certain sum of 7p.c.p.a for 4 years is rs 3584.what will be the compound interest on the same principle at 4 p.c.p.a in 2 years

Answer 1

$simple \: interest \: on \: a \: certain \: sum \: of \: 7 \: p.c.p.a \: for \: 4 \: years \: is \: rs \: 3584 \\ ci \: = p(1 + \frac{r}{100})^{n} \\ ci \: = 3584 \\ r = 7 \: p.c.p.a \\ n = 4 \: years \\ 3584 = p ({1 + \frac{7}{100} })^{4} \\ 3584 = p( \frac{107}{100})^{4} \\ 3584 = p ({1.07})^{4} \\ p = \frac{3584}{ {1.07}^{4} } \\ p = 2734 \\ compound \: interest \: on \: the \: same \: principle \: at \: 4 \: p.c.p.a \: in \: 2 \: years \\ ci = p ( 1 + \frac{r}{100}) ^{n} \\ p = 2734 \\ r = 4 \: p.c.p.a \\ n =2 \\ ci = 2734(1 + \frac{4}{100} )^{2} \\ ci = 2734( \frac{104}{100} )^{2} \\ ci = 2734( {1.04})^{2} \\ ci = 2734 \times 1.0816 \\ ci = 2957$