Question

4. The difference between the compound interest and the simple interest on a sum of money for
1.5 years at 12% per annum is 150. Calculate the amount​

Answer 1

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

${\bold{\therefore Principal=300\:rupees}}$

${\bold{\therefore Amount=504\:rupees}}$

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

$\underline \bold{Given : } \\ \implies Time(t) = 1.5 \: years \\ \\ \implies Rate(r) = 12\% \\ \\ \implies Difference = 150 \: rupees \\ \\ \underline \bold{To \: Find : } \\ \implies Amount = ?$

• According to given question :

$\bold{For \: Simple \: Interest : } \\ \implies S.I = \frac{p \times r \times t}{100} \\ \\ \implies S.I = \frac{p \times 12 \times 1.5}{100} \\ \\ \implies S.I = \frac{18p}{100} \\ \\ \bold{\implies S.I= 0.18 \: p} \\ \\ \bold{For \: Compound \: Interest : } \\ \implies A= p \times (1 + \frac{r}{100} )^{t} \\ \\ \implies A = p \times (1 + \frac{12}{100} ) ^{1.5} \\ \\ \implies A = p \times (1 + 0.12) ^{1.5} \\ \\ \implies A = p \times (1.12)^{1.5} \\ \\ \implies A = p \times 1.12 + 0.56 \\ \\ \bold{\implies A = 1.68p} \\ \\ \bold{For \: Compound \: Interest}\\ \implies C.I = A- p \\ \\ \implies C.I= 1.68p - p \\ \\ \bold{\implies C.I= 0.68 p} \\ \\ \bold{For \: Difference : } \\ \implies Difference = C.I-S.I\\ \\ \implies 150 = 0.68p - 0.18p \\ \\ \implies 150 = 0.50 \: p \\ \\ \implies p = \frac{150 \times 10}{5} \\ \\ \bold{\implies p = 300 \: rupees} \\ \\ \bold{For \: Amount : } \\ \implies A = 1.68p \\ \\ \implies A = 1.68 \times 300 \\ \\ \bold{\implies A = 504 \: rupees}$

Answer 2

Answer:

principal =Rs.20833.33

AMOUNT AT COMPOUND INTEREST = Rs 24733.32

AMOUNT AT SIMPLE INTEREST=RS 24583.32

Step-by-step explanation: