Question

Find the principal amount for the rare of interest $10$% p.a..time $3$ years and compound interest earned is Rs.$993$.

Answer 1

Rate of interest, r = 10% $=\frac{10}{100}=0.1$

Time period, $t\Rightarrow 3$years.

number of times compounded yearly, n = 1.

compounded interest = Rs 993.

$\therefore$ Amount A = principal + compound interest

= P + 993.

we know, A $=P(1+\frac{r}{n}{)}^{nt}$

$P+993=P(1+\frac{0.1}{1}{)}^3$

$P+993=P(1.1{)}^3$

$P+993=1.331P.$

$\Rightarrow 993=1.331P-P$

$\Rightarrow 0.33P=993.$

$\Rightarrow P=\frac{993}{0.331}$

$\Rightarrow P=Rs3000$