## APTITUDE PREPARATION: SIMPLE & COMPOUND INTEREST

#### Simple Interest (SI):

It is the amount earned by the principal only.
Simple interest earned over a certain period is a fixed percentage of the principal amount.
It is calculated by multiplying the principal amount by the interest rate and the number of periods in a loan.
SI=(PnR/100) where,
P-Principal Amount; n-Number of Periods, R-Rate of Interest per Period in %

#### Compound Interest (CI):

Compound interest is based on the principal amount and the accumulated interest.
It is interest over the interest also.
It is calculated by multiplying the principal amount by the annual interest rate raised to the number of compound periods.
CI=P[(1+R/100)n]-P
Note:
Simple Interest=Compound Interest if the period n=1

#### Example 1:

Calculate the simple interest on Rs. 500 for 6 months at 2 paise per month?

#### Solution:

Rate of Simple Interest=2 paise per 1 rupee per month (or) 2 rupees per 100 rupees per month
P=500, n=6 and R=2%
SI=(PnR/100) =(500x6x2/100) = Rs. 60

#### Example 2:

Calculate the compound interest on Rs. 500 for 6 months at 2 paise per month?

#### Solution:

Rate of Compound Interest=2 paise per 1 rupee per month (or) 2 rupees per 100 rupees per month
P=500, n=6 and R=2%
CI=P[(1+R/100)n]-P = 500[(1+2/100)6]-500 = 563.08-500=Rs. 63.08

#### Example 3:

A sum of money doubles itself in 7 years, it becomes 5 times in how many years?

#### Solution:

Assume a principal amount of Rs. 100.
It becomes 200 after 7 years.
To become Rs 500, ie., five times the initial amount of Rs. 100; an interest of Rs. 400 has to be added to the initial amount.
To get Rs. 100 we require 7 years and hence, to accumulate Rs. 400 we require 4×7=28 years.

#### Example 4:

A sum of money, P is lent at 4 percent simple interest per year, and in 8 years the interest accounted to Rs. 340 less than the sum lent. What is the sum lent?

#### Solution:

No of periods, n=8 years, Rate of Simple Interest, R=4% per year=4/100=0.04
SI=(PnR/100) =(Px8x0.04) =0.32P
0.32P=P-340
0,68P=340 and P=Rs. 500

#### Example 5:

The compound interest on a certain sum of money for 2 years is Rs. 52 and the simple interest for 2 years at the same rate is Rs. 50. What is the rate of interest?

#### Solution:

The difference of (52-50)=2 is the interest of the simple interest amount of first year.
Simple interest for 2 years=50 and for the first year=(50/2)=25
That is, simple interest of 25 for one year is 2.
SI=(25x1xR/100)=2 or (R/4)=2 or R=8% per year.

#### Example 6:

Calculate the simple interest rate, at which Rs. 200 will produce a total amount of Rs. 1000 after 40 years,

#### Solution:

Principal, P=200, No of Periods, n=40 years
Total amount after 40 years=1000
Simple interest after 40 years=(1000-200)=800
That is, (PnR/100) = 800
(200x40xR/100)=800
Rate of interest, R=(800×100/8000)=10% per year

#### Example 7:

A sum of Rs.15625 yields a compound interest of Rs.1951 in 3 years. Find the rate of interest.

#### Solution:

Let the number of employees = x.
CI= P[(1+R/100)n]-P=15625[(1+R/100)3]-15625=1951
[(1+R/100)3]=(17576/15625)=(26/25)3
(1+R/100)=(26/25)
R/100=(26/25)-1=(1/25)
Rate of interest, R=(100/25)=4% per year

#### Example 8:

Find the compound interest on Rs. 10000 in 2 years at 4% per annum, the interest being compounded half-yearly.

#### Solution:

Period, n=Number of half years=(2×2)=4
Rate of compound interest, R=4% per annum=2% per half year
Principal, P=10000
CI= P[(1+R/100)n]-P=10000[(1+2/100)4]-10000=10000[(1.02)4]-10000
= 824.32

#### Example 9:

A sum of money amounts to Rs. 9800 after 5 years and Rs. 12005 after 8 years at the same simple rate of interest. What is the interest rate?

#### Solution:

SI=(PnR/100) and,
Total amount=P+(PnR/100)
After 5 years: n=5
P+(Px5xR/100)=9800 or
P(1+R/20)=9800 …(i)
After 8 years: n=8
P+(Px8xR/100)=12005 or
P(1+R/12.5)=12005 …(ii)
Dividing equation (i) by (ii);
(1+R/20)/(1+R/12.5)=(9800/12005)
Cross multiplying;
12005(1+R/20)=9800(1+R/12.5)
12005+600.25R=9800+784R
183.75R=2205
Rate of interest, R=12% per year

#### Example 10:

Anand invested an amount of Rs. 13,900 divided in two different schemes A and B at the simple interest rate of 14% p.a. and 11% p.a. respectively. If the total amount of simple interest earned in 2 years be Rs. 3508, what was the amount invested in Scheme B?

#### Solution:

We have to estimate the principal amount in Scheme B=P.
Scheme A:
Principal=(13900-P), No of periods, n=2 years, Rate of interest, R=14% per year=14/100
SI=[(13900-P)x2x14/100)]=28(13900-P)/100 … (i)
Scheme B:
Principal=P, No of periods, n=2 years, Rate of interest, R=11% per year=11/100
SI=(Px2x11/100)]=22P/100 … (ii)
Total SI=[28(13900-P)/100] + [22P/100] =3508
28(13900-P)+22P=350800
389200-28P+22P=350800
6P=38400
P=6400.