Question

An amount of Rs. 1250 is compounded
annually at the rate of 20 % Decrease p.a. The amount
to be paid after 3 months would be ?​

Answer 1

Answer:

Example

A sum of Rs 20,000 is borrowed by Heena for 2 years at an interest of 8% compounded annually. Find the Compound Interest (C.I.) and the amount she has to pay at the end of 2 years. 

Aslam asked the teacher whether this means that they should find the interest year by year. The teacher said ‘yes’, and asked him to use the following steps :

 

1.  Find the Simple Interest (S.I.) for one year.

 Let the principal for the first year be P1. Here, P1 = Rs 20,000

 SI1 = SI at 8% p.a. for 1st year = Rs 

 

 2.  Then find the amount which will be paid or received. This becomes principal for the next year.

 Amount at the end of 1st year = P1 + SI1 = Rs 20000 + Rs 1600

 = Rs 21600 = P2 (Principal for 2nd year)

 

 3.  Again find the interest on this sum for another year.

 SI2 = SI at 8% p.a.for 2nd year = Rs 

 =  Rs 1728

 

 4. Find the amount which has to be paid or received at the end of second year.

 Amount at the end of 2nd year = P2 + SI2

 = Rs 21600 + Rs 1728

 = Rs 23328

 Total interest given = Rs 1600 + Rs 1728

 = Rs 3328

 

Reeta asked whether the amount would be different for simple interest. The teacher told her to find the interest for two years and see for herself.

SI for 2 years  

Reeta said that when compound interest was used Heena would pay Rs 128 more. Let us look at the difference between simple interest and compound interest. We start with Rs 100. Try completing the chart.

 

  Under Simple InterestUnder Compound InterestFirst yearPrincipalRs 100.00Rs 100.00 Interest at 10%Rs 10.00Rs 10.00 Year-end amountRs 110.00Rs 110.00Second yearPrincipalRs 100.00Rs 110.00 Interest at 10%Rs 10.00Rs 11.00 Year-end amountRs(110 + 10) = Rs 120Rs 121.00Third yearPrincipalRs 100.00Rs 121.00 Interest at 10%Rs 10.00Rs 12.10 Year-end amountRs(120 + 10) = Rs 130Rs 133.10

 

 Note that in 3 years, 

Interest earned by Simple Interest = Rs (130 – 100) = Rs 30, whereas,

Interest earned by Compound Interest = Rs (133.10 – 100) = Rs 33.10

Note also that the Principal remains the same under Simple interest, while it changes year after year under compound interest.