Question

The compound interest on a sum of money for 2 years is 1331-20 and the simple
interest on the same sum for the same period and at the same rate is 1250. Find the
sum and the rate of interest per annum.​

Answer 1

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

$\green{\tt{\therefore{Principal=4822.53\:rupees}}}$

$\green{\tt{\therefore{Rate=12.96\%}}}$

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

$\green {\underline \bold{Given :}} \\ \tt{: \implies Time(T) = 2 \: years} \\ \\ \tt{: \implies Compound \: interest(C.I) = 1331\:rupees} \\ \\ \tt{: \implies Simple\: interest(S.I) = 1250\:rupees} \\ \\ \red {\underline \bold{To \: Find :}} \\ \tt{: \implies Principal(P) =? } \\ \\ \tt{: \implies Rate(R) =? }$

• According to given question :

$\bold{As \: we \: know \: that} \\ \tt{: \implies S.I = \frac{P \times R \times T}{100} } \\ \\ \tt{: \implies 1250 = \frac{x \times R \times 2}{100} } \\ \\ \tt{: \implies 62500 = x \times r} \\ \\ \tt{: \implies R= \frac{62500}{x}} - - - - - (1) \\ \\ \bold{As \: we \: know \: that} \\ \tt{: \implies C.I = A- P} \\ \\ \tt{: \implies 1331 = A - x } \\ \\ \tt{: \implies A = 1331 + x} - - - - - (2) \\ \\ \bold{As \: we \: know \: that} \\ \tt{: \implies A = P(1 + \frac{r}{100} )^{T} } \\ \\ \text{Putting \: value \: of \: A \: from \: (2)} \\ \tt{: \implies 1331 + x = x(1 + \frac{r}{100})^{2} } \\ \\ \text{Putting \: value \: of \: r \: from \: (1)}\\ \tt{: \implies 1331 + x = x(1 + \frac{ \frac{62500}{x} }{100} )^{2} } \\ \\ \tt{: \implies 1331 + x = x(1 + \frac{62500}{x \times 100} )^{2}} \\ \\ \tt{: \implies 1331 + x = x (\frac{x + 625 }{x})^{2} } \\ \\ \tt{: \implies 1331 + x = \frac{ {x}^{2} + 390625 + 1250x}{x} } \\ \\ \tt{: \implies 1331x + {x}^{2} = {x}^{2} + 390625 + 1250x} \\ \\ \tt{: \implies 1331x - 1250x = 390625} \\ \\ \tt{: \implies 81x = 390625} \\ \\ \tt{: \implies x = \frac{390625}{81} } \\ \\ \green{\tt{: \implies x = 4822.53\:rupees}} \\ \\ \text{putting \: value \: of \: P \: in \: (1)}\\ \tt{: \implies R = \frac{62500}{4822.53}} \\ \\ \green{\tt{: \implies R = 12.96\%}}$

Answer 2

Answer:

Given:

The compound interest on a sum of money for 2 years is 1331 - 20. The simple interest on the same sum for the same period and at the same rate is 1250.

Find:

Find the sum and the rate of interest per annum.

Know terms:

(T) = Time.

(CI) = Compound interest.

(SI) = Simple interest.

(P) = Principal amount.

(R) = Rare percentage (℅)

Calculations:

(T) = 2 YEARS

(CI) = ₹1331

(SI) = ₹1250

Note:

(₹) Symbol of rupees.

Let us assume principal as "x".

Further calculations:

Using formula:

= SI = P × R × T/100

Using the above formula, further calculations.

= 1250 = (x) × (R) × (2)/100

= 62500 = x + r

= R = 62500/x – Equation (1)

= CI = A - P

= 33 = A - x

= A = 1331 + x – Equation (2)

Using another formula:

= P (1 + R/100)^n

Note:

- (n) = time period.

- This is used when the amount when interest is compound annually.

Adding the values for equation (2);

= 1331 + x = x (1 + 62500/x/100)^2

= 1331 + x = x (x + 62500/x × 100)^2

= 1331 + x = x^2 + 390625 + 1250x/x

= 1331 x + x^2 = x^2 + 390625 + 1250 x

= 1331 x - 1250 x = 390625

= 81 x = 390625

= x = 390625/81

= x = ₹4822.53

Adding the values for equation (1);

= R = 62500/4822.53

= R = 12.96 %