Question

the compound interest on a certain sum of money invested for 2years at 5% is ₹238.what will be the simple interest on it at the same rate and for the same period ?​

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{Simple\:Interest=232.195\:rupees}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given:}} \\ \tt: \implies Compoud \:Interest(C.I) = 238 \\ \\ \tt: \implies Time(t)= 2 \: years \\ \\ \tt: \implies Rate(r) = 5\% \\ \\ \red{\underline \bold{To \: Find:}} \\ \tt: \implies Simple \: Interest(S.I) = ?$

• According to given question :

$\bold{As \: we \: know \: that} \\ \tt: \implies C.I = A - p \\ \\ \tt: \implies 238 = A - p \\ \\ \tt: \implies A = 238 + p \\ \\ \bold{As \: we \: know \: that} \\ \tt: \implies A = p(1 + \frac{r}{100})^{t} \\ \\ \tt: \implies 238 + p = p(1 + \frac{5}{100})^{2} \\ \\ \tt: \implies 238 + p = p(1 + 0.05)^{2} \\ \\ \tt: \implies 238 + p = p \times 1.1025 \\ \\ \tt: \implies 238 = 1.1025p - p \\ \\ \tt: \implies p = \frac{238}{0.1025} \\ \\ \green{\tt: \implies p = 2321.95 \: rupees} \\ \\ \bold{As \: we \: know \: that} \\ \tt: \implies S.I= \frac{p \times r \times t}{100} \\ \\ \tt: \implies S.I= \frac{2321.95 \times 5 \times 2}{100} \\ \\ \green{\tt: \implies S.I = 232.195 \: rupees}$

Answer 2

Answer:

★ Simple Interest = Rs 232.195 ★

Step-by-step explanation:

Given:

• Compound Interest is Rs 238
• Rate is 5%
• Time is 2 years

To Find:

• Simple interest

Solution:

★ Compound Interest = Amount – Principal ★

$\small\implies{\sf }$ Rs 238 = A – P

$\small\implies{\sf }$ 238 + P = A

★ Formula for finding Amount = Amount = Principal ( 1 + r/100)^n ★

$\small\implies{\sf }$ 238 + P = P ( 1 + r/100)^n

$\small\implies{\sf }$ 238 + p = p ( 1 + 5/100)²

$\small\implies{\sf }$ 238 + p = p ( 1 + 0.05)²

$\small\implies{\sf }$ 238 + p = p (1.05)²

$\small\implies{\sf }$ 238 + p = p x 1.1025

$\small\implies{\sf }$ 238 + p = 1.1025p

$\small\implies{\sf }$ 238 = 1.1025 – p

$\small\implies{\sf }$ 238 = 0.1025p

$\small\implies{\sf }$ 238/0.1025 = p

$\small\implies{\sf }$ Rs 2321.95 = P

★ Simple Interest = Principal x Rate x Time / 100 ★

$\small\implies{\sf }$ S.I = 2321.95 x 5 x 2 / 100

$\small\implies{\sf }$ S.I = 23219.5 / 100

$\small\implies{\sf }$ S.I = Rs 232.195

Hence, The Simple Interest will be Rs 232.195