Find the Amount to be paid at the end of 2 years when p ₹ 6400 and r 6 pa

Solution:

Amount (A) = P[1 + (r/100)]n

Principal (P) = ₹ 26400

Time period (n) = 2 years 4 months

Rate % (R) = 15% compounded annually

Steps:

Firstt, we will calculate Compound Interest (C.I) for the period of 2 years

A = P[1 + (r/100)]n

= 26400[1 + (15/100)]2

= 26400[(100/100) + (15/100)]2

= 26400 × 115/100 × 115/100

= 26400 × 23/20 × 23/20

= 26400 × 1.3225

= 34914

C.I. = A - P

= 34914 - 26400

= 8514

Now, we will find Simple Interest (S.I) for the period of 4 months

Principal for 4 months after C.I. for 2 years = ₹ 34,914

We know that,

S.I = PRT/100

Here T = 4 months = 4/12 years = 1/3 years

S.I. for 4 months = (1/3) × 34914 × (15/100)

= (1/3) × 34914 × (3/20)

= 34914/20

= 1745.70

Total interest for 2 years 4 months = 8514 + 1745.70

= 10259.70

Total amount for 2 years 4 months = 26400 + 10259.70

= ₹ 36659.70

☛ Check: NCERT Solutions for Class 8 Maths Chapter 8

Video Solution:

Kamala borrowed ₹ 26400 from a Bank to buy a scooter at a rate of 15% p.a. compounded yearly. What amount will she pay at the end of 2 years and 4 months to clear the loan? (Hint: Find A for 2 years with interest is compounded yearly and then find SI on the 2nd year amount for 4/12 years.)

NCERT Solutions Class 8 Maths Chapter 8 Exercise 8.3 Question 2

Summary:

Kamala borrowed ₹ 26400 from a Bank to buy a scooter at a rate of 15% p.a. compounded yearly. The amount Kamala will have to pay after 2 years 4 months to clear the loan is ₹ 36659.70.

☛ Related Questions:

Math worksheets and
visual curriculum

In simple interest we will learn about how to calculate simple interest. We will recapitulate the formula for simple interest and know more about it. When we borrow money from any source (bank, agency, moneylender), we have to pay back the money after a certain period along with extra money for availing the facility to use the money borrowed.

What is Simple Interest?

● The money borrowed is called the principal (P).

● Extra money paid back is called the simple interest (S.I).

● Interest is expressed as rate par cent per annum (p.a.) i.e., 12% per month means, the interest on $100 for 1 year is $12.

● The total money paid back after the given time is called the amount.

● Time for which money is borrowed is called the time period.

We already know what is simple interest and while calculating the time period we need to:

Day on which money is borrowed is not counted but the day which the money is returned is counted.

When number of day is converted into year, we always divide the number of days by 365, whether it is a leap year or an ordinary year.

Here,

P = Principal

R = rate% per annum
T = time
I = simple interest
A = amount
Formula for calculating simple interest is S.I = (P × R × T)/100

Important: Formula for calculating amount is A = P + I

Examples on simple interest:

What is Simple Interest?

1. Find simple interest on $2000 at 5% per annum for 3 years. Also, find the amount.

Solution:

Principal = $2000Rate = 5% p.a. T = 3 yearsS.I = (P × R × T)/100

= (2000 × 5 × 3)/100

= $ 300

Amount = P + I = $ ( 2000 + 300 ) = $ 2300

2. Calculate the simple interest on $ 6400 at 10% p.a. for 9 months.

Solution:

P = $ 6400R = 10% p.a.T = 9 months or 9/12 years [12 months = 1 year

1 months = 1/12 years

9 months = (1 × 9)/12 years] Therefore, S.I. = (P × R × T)/100 = (6400 × 10 × 9)/(100 × 12)

= $480

3. Mike took a loan of $20000 from a bank on 4 February 2009 at the rate of 8% p.a. and paid back the same on 6th July 2009. Find the total amount paid by Mike. P = $20000 R = 8 % p.a. T = 152/365

Solution:

Time = February + March +April + May + Jun + July = 24 days + 31 days + 30 days + 31 days + 30 days + 6 days = 152 days Therefore, S.I. = (P × R × T)/100 = (20000 × 8 × 152)/(100 × 365) = $ (40 × 8 × 152)/73 = $ 666.30 Therefore, the amount paid = $ (20,000 + 666.30) = $ 20666.30

What is Simple Interest?

4. At what per cent will $ 1500 amount to $ 2400 in 4 years?

Solution:

P = $ 1500 R = ? T= 4 years and A = $ 2400 S.I. = A - P = $(2400 - 1500 ) = $ 900 S.I. = (P × R × T)/100 900 = (1500 × R × 4)/100 Therefore, R = (900 × 100)/(4 × 1500) = 15%

5. In how much time will a sum of money triple itself at 15 % p.a.?

Solution:

Let P = x, then A = 3x So, I = A - P = 3x - x = 2x We know that S.I = (P × R × T)/100 2x = (x × 15 × T)/100 T = (2x × 100)/(x × 15) = 40/3 = 13.3 years

6. At what rate percent per annum simple interest will a sum of money double itself in 6 years?

Solution:

Let P = x, then A = 2x Also, S.I = A - P = 2x - x = x T = 6 years We know that S.I. = (P × R × T)/100 (x × R × 6)/100 = x R = 100x/6x = 16.6 %

What is Simple Interest?

7. A some amounted to $ 2520 at 10% p.a. for the period of 4 years. Find them sum.

Solution:

Let A = $ 2520 R = 10% p.a. T = 4 years P = ? Let the principal be x S.I = (x × 10 × 4)/100 = 2x/5 A = P + I A = x + 2x/5 A = (5x + 2x)/5 = 7x/5 [But given that A = $2520] 7x/5 = 2520 7x = 2520 × 5 x = (2520 × 5)/7 = $ 1800

8. Ron borrowed $ 24000 from his friend at the rate of 12% per annum for 3 years. At the end of the period, he cleared the account by paying $ 10640 cash and giving the cow. Find the price of the cow.

Solution:

Here, P = $24000 R = 12% p.a. T = 3 years S.I. = (P × R × T)/100 = (24000 × 12 × 3)/100 = $ 8640 Amount = $24000 + 8640 = $ 32640 Now, $10640 + Price of cow = $ 32460 Therefore, price of the cow = $ 32460 - 10640 = $ 22000

What is Simple Interest?

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What is Simple Interest?

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Answer

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Hint: To calculate S.I and amount, we use the formula of S.I to get interest and then using interest, we calculate the sum on the given principal.

Formula used: \[S.I = \dfrac{{P \times R \times T}}{{100}}\] ,

\[\begin{array}{*{20}{l}} {P = Principal,} \\ {R = Rate{\text{ }} of {\text{ }}interest,} \\ {T = time} \end{array}\]

Complete step by step answer:

As given,Principal \[\left( P \right) = 6400\] Rate \[\left( R \right) = 6\% {\text{ }}p.a.\] Time \[\left( T \right) = 2{\text{ }} years\] (1) Let interest be the S.I on the given principal amount of Rs. \[6400\] ∴ by S.I formula, we have\[S.I = \dfrac{{P \times R \times T}}{{100}}\] Where P is principal, R is rate per annum. T is time.(2) Using values of P, R and T in the formula mentioned in step \[1\] to get S.I.\[S.I = 6400 \times \dfrac{6}{{100}} \times 2\] \[ = 64 \times 6 \times 2\] \[ = 64 \times 12\] \[S.I = Rs.768\] (3) Hence interest on Rs.\[6400\] for $2$ years at 6% p.a. is Rs.\[768.\] (4) Now to calculate the amount. We know that amount that a person receives after $2$ years on Rs.\[6400\] at 6% will be the sum of principal and interest on it.\[\therefore A = P + I\] Using value of \[P = {\text{ }}6400,\,\,\;S.I = Rs.768\] \[ \Rightarrow A = 6400 + 768\]\[ = Rs.7168\]

Additional Information: Simple interest is interest calculated on the principal portion of a loan or the original contribution to a savings account. Simple interest does not compound, meaning that an account holder will only gain interest on the principal, and a borrower will never have to pay interest on interest already accrued.

Note: In case if time is either in months or days then we convert it first in year after dividing by $12$ months or \[365\] days as rate is given in per annum.