Question

the difference between compound interest and simple interest for a certain sum of money for 3 years at 5% per annum is rupees 61 find the sum

Answer 1

Here is your answer for the problem.

Answer 2

▶ Question :-

→ The difference between compound interest and simple interest for a certain sum of money for 3 years at 5% per annum is ₹ 61, Find the sum .


▶ Answer :-

→ ₹8000 .


▶ Step-by-step explanation :-

➡ Given :-

→ Rate = 5 % per annum .

→ Time = 3 years .

→ CI - SI = ₹61 .


➡ To Find :-

→ Sum ( p ) .


$\huge \pink{ \mid{ \underline{ \overline{ \tt Solution :- }} \mid}}$


For CI ,

$\sf \because Amount = p \bigg(1 + \frac{r}{100} \bigg)^{t} .$


And, For SI ,


$\sf \because Amount = p + \frac{prt}{100} .$


▶ Now,

°•° CI - SI = ₹61 .

$\sf \implies p \bigg(1 + \frac{r}{100} \bigg) ^{t} - \bigg(p + \frac{prt}{100} \bigg) = 61. \\ \\ \sf \implies p \bigg((1 + \frac{r}{100} ) ^{t} - 1 - \frac{rt}{100} \bigg) = 61. \\ \\ \sf \implies p \bigg((1 + \frac{5}{100} ) ^{3} - 1 - \frac{5 \times 3}{100} \bigg) = 61. \\ \\ \sf \implies p \bigg((1 + 0.05)^{3} - 1 - 0.15 \bigg) = 61. \\ \\ \sf \implies p(7.625 \times {10}^{ - 3} ) = 61. \\ \\ \sf \implies p = \frac{61 \times 10 \times 10 \times 10}{7.625} . \\ \\ \huge \orange{ \boxed{ \boxed{ \tt \therefore p = 8000.}}}$



✔✔ Hence, the sum is ₹8000 ✅✅ .



THANKS