Simple and Compound Interest  Aptitude basics, practice questions, answers and explanations 
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Important formula and equations

Principal: The money borrowed or lent out for a certain period is called the principal or the sum.
Interest: Extra money paid for using other's money is called interest.
Simple Interest (SI): If the interest on a sum borrowed for certain period is reckoned uniformly, then it is called simple interest.

Let Principal= P, Rate= R% per annum (p.a) and Time= T years. Then 
(i) Simple Interest= (P*R*T)/100
(ii) P = (100*SI)/(R*T); R= (100*SI)/(P*T) and T= (100*SI)/(P*R)

Key notes on Simple Interest

A sum of money becomes n times itself in T years at simple interest, then the rate of interest is 
Rate= 100(n-l)%
               T 
If a sum of money becomes n times in T years at SI then it will be m times of itself in ..... years
Required time= (m-l)*T years
                          (n-l) 
If SI on a sum of money is 1/xth of the principal and the time T is equal to the rate percent R, then
Rate= Time=
A certain sum is at SI at a certain rate for T years. And if it had been put at R1 % higher rate, then it would fetch Rs.x more, then the 
Principal= x*100
                 T*R1
The annual payment that will discharge a debt of Rs.P due in T years at the arte of interest R% per annum is Annual payment =
100P               
100T+RT(T-1)
                   2    
                                                                               
Let the rate of interest for first 1 years is r1% per annum, for the next t2 years is r2 % per annum and for the period beyond that is r3 %. Suppose all together the simple interest for t3 years is Rs.I. Then Principal=100*I                         
                         t1r1+t2r2+(t3-t1-t2)r3
The simple interest on a certain sum of money at r1 % per annum for t1 years is Rs.m. The interest on the same sum for t2 years at r2 % per annum is n.
Then the sum= (m-n)*100
                         r1t1-r2t2

Key notes on Compound interest

Compound Interest: (Amount - Principal)
Amount= P* (1+R/100)ⁿ 
When the interest is compounded K times a year, Amount= P( 1 + R / K*100)^kt
When the interest is paid half yearly, say at r%per annum compound interest, then the amount after t years is given by: 
P( 1 + R / 2*100)^2t 
Similarly, if the interest is paid quarterly, say at r% per annum compound interest, then the amount due after t years is given by: 
P( 1 + r / 4 * 100)^4t

Under the method of equated instalments, the value of each instalment is the same.

Equal Annual Instalment under
(a) Simple Interest, x = 2P(100 + nr)
                                     n[200 + (n - 1)r]
(b) Compound Interest, x = Pr / 100[1 – (100/100 + r) ⁿ ]



Exercise questions

1.A father left a will of Rs.35 lakhs between his two daughters aged 8.5 and 16 such that they may get equal amounts when each of them reach the age of 21 years. The original amount of Rs.35 lakhs has been instructed to be invested at 10% p.a. simple interest. How much did the elder daughter get at the time of the will?
A) Rs.17.5 lakhs 
B)Rs.21 lakhs 
C) Rs.15 lakhs 
D) Rs. 20 lakhs

2.What will Rs.1500 amount to in three years if it is invested in 20% p.a. compound interest, interest being compounded annually?
A) 2400 
B) 2592 
C) 2678 
D)2540

3. If a sum of money grows to 144/121 times when invested for two years in a scheme where interest is compounded annually, how long will the same sum of money take to treble if invested at the same rate of interest in a scheme where interest is computed using simple interest method?
A) 9 years 
B) 22 years 
C) 18 years 
D)33 years

4. The population of a town was 3600 three years back. It is 4800 right now. What will be the population three years down the line, if the rate of growth of population has been constant over the years and has been compounding annually?
A) 6000 
B) 6400 
C) 7200 
D)9600

5. A man invests Rs.5000 for 3 years at 5% p.a. compound interest reckoned yearly. Income tax at the rate of 20% on the interest earned is deducted at the end of each year. Find the amount at the end of the third year.
A) 5624.32 
B)5630.50 
C)5788.125 
D)5627.20

6. The difference between the compound interest and the simple interest on a certain sum at 12% p.a. for two years is Rs.90. What will be the value of the amount at the end of 3 years?
A) 9000 
B) 6250 
C) 8530.80 
D)8780.80

7. Vijay invested Rs.50,000 partly at 10% and partly at 15%. His total income after a year was Rs.7000. How much did he invest at the rate of 10%?
A) Rs.40,000 
B)Rs.40,000 
C)Rs.12,000 
D)Rs.20,000

8. A sum of money invested for a certain number of years at 8% p.a. simple interest grows to Rs.180. The same sum of money invested for the same number of years at 4% p.a. simple interest grows to Rs.120 only. For how many years was the sum invested?
A) 25 years 
B) 40 years 
C) 33 years and 4 months 
D)Cannot be determined

9. How long will it take for a sum of money to grow from Rs.1250 to Rs.10,000, if it is invested at 12.5% p.a simple interest?
A) 8 years 
B) 64 years 
C) 72 years 
D)56 years

10. Rs.5887 is divided between Shyam and Ram, such that Shyam's share at the end of 9 years is equal to Ram's share at the end of 11
years, compounded annually at the rate of 5%. Find the share of Shyam.
A) 2088 
B) 2000 
C) 3087 
D)None of these

Answer Key

1.B; 2.B; 3.B; 4.B; 5.A; 6.D; 7.B; 8.A; 9.D; 10.C