Question

Question 42
The simple interest at 10% pa for 2 years
on a certain principal is Rs. 800. Find the
compound interest on the same amount
at the same rate of interest for the same
period
Rs 4,840
R 800
Ro
RO BAO
RS4800​

Answer 1

Answer:

Compound Interest = Rs 840

Step-by-step explanation:

Given that:

• Simple interest = Rs 800
• Rate of interest = 10% p.a.
• Time = 2 years

Formula for Simple Interest:

S.I. = (p × r × t)/100

Where,

★ S.I. = Simple Interest

★ p = Principal

★ r = Rate of interest

★ t = Time

★ A = Amount

Let's find the principal:

800 = (p × 10 × 2)/100

➤ 20p = 800 × 100

➤ p = 80000/20

➤ p = 4000

∴ Principal = Rs 4000

Now,

Find the compound interest on the same amount at the same rate of interest for the same period.

Formula to find Compound Interest:

C.I. = A - p

Where, C.I. = Compound Interest

So, firstly we should find Amount:

A = p(1 + r × 0.01)ᵗ

Finding the amount:

A = 4000(1 + 10 × 0.01)²

➤ A = 4000(1 + 0.1)²

➤ A = 4000 × 1.1 × 1.1

➤ A = 4840

∴ Amount = Rs 4840

It's the time to find C.I.:

C.I. = A - p

➤ C.I. = 4840 - 4000

➤ C.I. = 840

∴ Compound Interest = Rs 840

Answer 2

${\large{\bold{\rm{\underline{Correct \: question}}}}}$

★ The simple interest at 10% P.A for 2 years on a certain principal is Rs. 800. Find the compound interest on the same amount at the same rate of interest for the same period.

$\sf Given \: that \begin{cases} & \sf{Simple \: interest \: = \bf{800 \: Rupees}} \\ & \sf{Rate \: of \: interest \: = \bf{10 \: percentage}} \\ & \sf{Time \: = \bf{2 \: year's}} \end{cases}$

${\large{\bold{\rm{\underline{To \; find}}}}}$

★ The compound interest on the same amount at the same rate of interest for the same period

${\large{\bold{\rm{\underline{Solution}}}}}$

★ The compound interest on the same amount at the same rate of interest for the same period ↝ Rupees 840.

${\large{\bold{\rm{\underline{Using \; concepts}}}}}$

★ Formula to find Simple Interest

★ Formula to find amount when interest is compounded annually.

★ Formula to find Compound interest

${\large{\bold{\rm{\underline{Using \; formulas}}}}}$

${\sf{\star Simple \: interest \: = \: \dfrac{P \times R \times T}{100}}}$

$\; \; \; \; \; \; \; \; \; \; \;{\tt{Where,}}$

⚪P denotes Principal

⚪R denotes Rate

⚪T denotes Time

${\sf{\star P(1+ \dfrac{R}{100})^{n}}}$

$\; \; \; \; \; \; \; \; \; \; \;{\tt{Where,}}$

⚪P denotes Principal

⚪R denotes Rate

⚪n denotes time

${\sf{\star CI \: = Amount \: - Principal}}$

${\large{\bold{\rm{\underline{Full \; Solution}}}}}$

~ Let's use the formula to find Simple Interest and implied the values and let us find Principal..!

${\sf{:\implies Simple \: interest \: = \: \dfrac{P \times R \times T}{100}}}$

${\sf{:\implies 800 \: = \: \dfrac{P \times 10 \times 2}{100}}}$

${\sf{:\implies 800 \: = \: \dfrac{P \times 20}{100}}}$

${\sf{:\implies 800 \: = \: \dfrac{P \times 2}{10}}}$

${\sf{:\implies 800 \: = \: \dfrac{P}{5}}}$

• ( × = ÷ ) ; ( ÷ = × )

${\sf{:\implies 800 \times 5 \: = P}}$

${\sf{:\implies 4000 \: = P}}$

${\sf{:\implies P \: = Rupees \: 4000}}$

${\frak{Henceforth, \: Rupees \: 4000 \: is \: Principal}}$

~ Now let's find the compound interest on the same amount at the same rate of interest for the same period by using formula to find Compound interest

~ Using formula = Amount when interest is compounded annually

${\sf{:\implies 4000(1+ \dfrac{10}{100})^{2}}}$

${\sf{:\implies 4000(1+ 0.1)^{2}}}$

${\sf{:\implies 4000(1.1)^{2}}}$

${\sf{:\implies 4000(1.1)(1.1)}}$

${\sf{:\implies 4000 \times 1.1 \times 1.1}}$

${\sf{:\implies 4000 \times 1.21}}$

${\sf{:\implies 4840 \: Rupees }}$

${\frak{Henceforth, \: Rupees \: 4840 \: is \: amount}}$

~ Now at last let's find Compound Interest..!

${\sf{:\implies CI \: = Amount \: - Principal}}$

${\sf{:\implies CI \: = 4840 - 4000}}$

${\sf{:\implies CI \: = 840}}$

${\frak{Henceforth, \: Rupee \: 840 \: is\: CI}}$

${\large{\bold{\rm{\underline{Additional \; knowledge}}}}}$

~ Sσmє mσrє knσwlєdgє rєlαtєd tσ tσpíc - Cσmpαríng Quαntítíєs

♛ Discount is a reduction given on market price.

◆ Discount = Marketed price - Sale price.

♛ Discount can be calculated when discount percentage is given.

◆ Discount = Discount percentage of Marketed Price

♛ Additional expenses made after buying an article are included in the cost price and are known to be “overhead expenses”

◆ CP = Buying Price + Overhead expenses.

♛ Sales tax is charged on sale of an item by the government and is added to the bill amount.

◆ Sale tax = Tax % of bill amount

♛ Some extra formulas -

◆ Amount when interest is compounded annually -

P(1+R/100)^n

◆ Amount when interest is compounded half yearly -

P(1+R/200)^2n

$\; \; \; \; \; \;{\bf{Where,}}$

↝ P denotes Principal

↝ R denotes rate of interest

↝ n denotes time

↝ R/2 denotes half yearly rate

↝ 2n denotes number of half year