Simple and Compound Interest Problems with Shortcut Methods - Introduction

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P.S : Sorry for the bad handwriting :P

Interest is the money paid for the use of money borrowed. The Sum borrowed is called the Principal. The Sum of Interest and Principal is called the Amount.

If the interest is paid as it falls due, it is called the Simple Interest (SI).

If P is the principal, R is the ratio; T is time and S.I is the Simple Interest, then,

Money is said to be lent at Compound Interest (C.I) if the interest is not paid as soon as falls due, but is added to the Principal after a fixed period, so that the amount at the end of period becomes the principal for the next period. If A is the Amount, C.I is the Compound Interest, P is the Principal, R is the Rate, and t is the Time then,

Important Points to Note :

1. If Interest is paid half yearly; Time is doubled and the Rate is halved.
2. If Interest is paid quarterly, time becomes 4 times
3. Compound Interest for one year is equal to the Simple Interest for one year

Difference Between Simple and Compound Interests

For 2 years

For 3 years

Now let's do some example problems...

Example 1 : A sum of money amounts to Rs. 944 in 3 years at a Simple Interest. If the ratio of interest be raised by 25% the sum amounts to 980 during the same period. Find the sum and the rate of interest.

Solution :

Rs. 980 - Rs. 944 = 36

25% interest = Rs. 36

100% = (36 x 100) / 25  = Rs. 144

Hence the interest of three years = Rs. 144

Therefore,

Principal = 944 - 144  = Rs. 800

Rate =  [(144 x 100) / (800 x 3)] = 6%

Example 2 : Mahajan lends out Rs. 9 on the condition that the loan is payable in 10 months by 10 equal installments or Re. 1. Find the rate of percent per annum.

Solution :

Let the Interest be Rs. x per month per rupee

Interest on Rs. 9 for 1 month = 9x

Interest on Rs. 8 for 1 month = 8x

Interest on Rs. 7 for 1 month = 7x

Interest on Rs. 6 for 1 month = 6x

Interest on Rs. 5 for 1 month = 5x

Interest on Rs. 4 for 1 month = 4x

Interest on Rs. 3 for 1 month = 3x

Interest on Rs. 2 for 1 month = 2x

Interest on Rs. 1 for 1 month = 1x

                        Total Interest = 45x

But, according to the problem this must be Re. 1

So, 45x = 1   or x = 1/45

Interest for 1 month on Re. 1 = 1/45

Interest for 12 month on Rs. 100 = (100 x 12)/45  =>  85/3  => 26 (2/3) %

Example 3 :  A man deposits Rs. 5,600 in a bank at 3(3/4) % annual interest. After 6 months he withdraws Rs. 3,200 together with interest and after 6 months the remaining money. How much does he get as Interest ?

Solution :

S.I for Rs. 5,600 for 6 months  =

He withdraw Rs. 3,200 together with interest, the remaining amount = 5600 - 3200 = Rs. 2400

S.I on Rs. 2,400 at the rate of 15/4 for 1/2 years

So, Total Interest = 105 + 45  = Rs. 150

Example 4 : Find the Simple Interest on Rs. 5200 for 2 years at 6% per annum.

Solution :

Here P = Rs. 5,200, T = 2 years and R = 6%

=> Simple Interest =  (P x R x T) / 100

= (5200 x 6 x 2) / 100

Example 5 : Find the Simple Interest on Rs. 300 at 6% per annum from March 3rd to May 15th in the same year.

Solution :

Time from March 3rd to May 15th  = 28 days of March + 30 days of April and 15 days of May

= 73 days =  73/365 years

= 1/5 years

=> S.I = (300 x 6 x 1/5) / 100

Example 6 : On what sum will the interest for 3 years at 4% per annum amount to Rs. 300 ?

Solution :

Here, T = 3   R = 4%

and S.I = 300

 we need P

so P = (300 x 100) / (3x4)

= Rs. 2500

That's it for now guys. I will share few more example problems with solutions. Please let me know my way of explaining is understandable or not. So that I can improve. Good Day :)

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