# IMPORTANT FORMULAS

1. Speed, Time and Distance:
Speed = (Distance/ Time), Time= (Distance/Speed), Distance = (Speed x Time).
Time Speed
2. km/hr to m/sec conversion:
x km/hr = x x 5/18 m/sec.
3. m/sec to km/hr conversion:
x m/sec = x x 18/5 km/hr.
4. If the ratio of the speeds of A and B is a : b, then the ratio of the
the times taken by then to cover the same distance is
1/a : 1/b or b : a.
5. Suppose a man covers a certain distance at x km/hr and an equal distance at y km/hr. Then,
the average speed during the whole journey is
(2xy/ x + y) km/hr.

## Compound Interest

Let Principal = P, Rate = R% per annum, Time = n years.

When interest is compound Annually:
Amount = P (1 + R/100) n
When interest is compounded Half-yearly:
Amount = P [1 + (R/2)/100] 2n
When interest is compounded Quarterly:
Amount = P [1 + (R/4)/100] 4n
When interest is compounded Annually but time is in fraction, say 3 years.
Amount = P [1 + R/100]3 x (1+ 2/5r/100)
When Rates are different for different years, say R1%, R2%, R3% for 1st, 2nd and 3rd year respectively.
Then, Amount = P (1 +r1/100)(r2/100)(1+r3/100)
Present worth of Rs. x due n years hence is given by:
Present Worth x=/(1+r/100)

### MCQS:

A bank offers 5% compound interest calculated on half-yearly basis. A customer deposits Rs.
1600 each on 1stJanuary and 1st July of a year. At the end of the year, the amount he would
have gained by way of interest is:

A. Rs. 120
B. Rs. 121
C. Rs. 122
D. Rs. 123
Explanation:
Amount = Rs. [1600 x (1 +5/2+100)2 +1600 x (1+5/2+100)
Rs [1600 x 41/40 x 41/40+1600 x 41/40] Rs [1600 x 41/40 (41/40 + 1)] Rs [1600 x 41 x 81/40 x 40] Rs. 3321 C.I = Rs. (3321-3200) Rs=121

The difference between simple and compound interests compounded annually on a certain sum
of money for 2 years at 4% per annum is Re. 1. The sum (in Rs.) is:

A. 625
B. 630
C. 640
D. 650
Explanation:
Let the sum be Rs. x. Then,
C.I. = [x (1 + 4/100)2-x]=[676/ 625 x-x]=51/625 x
S.I. = (x x 4 x 2/100) = 2x/25 51x/625 – 2x/25 = 1
x=625

There is 60% increase in an amount in 6 years at simple interest. What will be the compound
interest of Rs. 12,000 after 3 years at the same rate?

A. Rs. 2160
B. Rs. 3120
C. Rs. 3972
D. Rs. 6240
E. None of these
Explanation:
Let P = Rs. 100. Then, S.I. Rs. 60 and T = 6 years.
R = (100 x 60/100 x 6) = 10% p.a.
Now, P = Rs. 12000. T = 3 years and R = 10% p.a.
C.I. = [Rs. 12000 x {(1 +10/100)3 – 1}]
= Rs. (12000 x 331/1000)
= 3972

What is the difference between the compound interests on Rs. 5000 for 1 years at 4% per
annum compounded yearly and half-yearly?

A. Rs. 2.04
B. Rs. 3.06
C. Rs. 4.80
D. Rs. 8.30
Explanation:
C.I. when interest
compounded yearly
= Rs. 5000 x (1 + 4/100) x (1 + 1/2 x 4/100)]
= Rs. 5000 x 26/25 x 51/50
= Rs. 5304.
C.I. when interest is
compounded half-yearly
= Rs. [5000 x (1 + 2/100)3]
= Rs. (5000 x 51/50 x 51/50 x 51/50)
= Rs. 5306.04
Difference = Rs. (5306.04 – 5304) = Rs. 2.04

The compound interest on Rs. 30,000 at 7% per annum is Rs. 4347. The period (in years) is:
A. 2
B. 2 1/2
C. 3
D. 4
Explanation:
Amount = Rs. (30000 + 4347) = Rs. 34347. Let the time be n years. Then, 30000 (1 + 7/100)n = 34347 (107/100) = 34347/30000 = 11449/10000 = (107/100)2
n = 2 years.

What will be the compound interest on a sum of Rs. 25,000 after 3 years at the rate of 12
p.c.p.a.?

A. Rs. 9000.30
B. Rs. 9720
C. Rs. 10123.20
D. Rs. 10483.20
E. None of these
Explanation:
Amount = Rs. [25000 x (1 + 12/100)3]
= Rs. (25000 x 28/25 x 28/25 x 28/25
= Rs. 35123.20
C.I. = Rs. (35123.20 – 25000) = Rs. 10123.20

At what rate of compound interest per annum will a sum of Rs. 1200 become Rs. 1348.32 in 2 years?
A. 6%
B. 6.5%
C. 7%
D. 7.5%
Explanation:
Let the rate be R% p.a.
Then, 1200 x (1 + R/100)2 = 1348.32
(1+R/100)2 = 134832/120000 =11236/10000
(1 + R/100)2 = (106/100)2 1+ R/100 = 106/100
R = 6%

The least number of complete years in which a sum of money put out at 20% compound interest
will be more than doubled is:

A. 3
B. 4
C. 5
D. 6
Explanation:
P (1 + 20/100)n > 2P => (6/5)n > 2
Now, (6/5 x 6/5 x 6/5 x 6/5)>2
So, n = 4 years.

Albert invested an amount of Rs. 8000 in a fixed deposit scheme for 2 years at compound
interest rate 5 p.c.p.a. How much amount will Albert get on maturity of the fixed deposit?

A. Rs. 8600
B. Rs. 8620
C. Rs. 8820
D. None of these
Explanation:
Amount = Rs. [8000 x (1 + 5/100)2]
= Rs. (8000 x 21/20 x 21/20
= Rs. 8820.

The effective annual rate of interest corresponding to a nominal rate of 6% per annum
payable half-yearly is:

A. 6.06%
B. 6.07%
C. 6.08%
D. 6.09%
Explanation:
Amount of Rs. 100 for 1 year
when compounded half-yearly
= Rs. [100 x (1 + 3/100)2] = Rs. 106.09
Effective rate = (106.09 – 100)% = 6.09%

Simple interest on a certain sum of money for 3 years at 8% per annum is half the compound interest on Rs. 4000 for 2 years at 10% per annum. The sum placed on simple interest is:
A. Rs. 1550
B. Rs. 1650
C. Rs. 1750
D. Rs. 2000
Explanation:
C.I. = Rs. [4000 x (1 + 10/100)2 – 4000]
= Rs. (4000 x 11/10 x 11/10 – 4000)
= Rs. 840.
Sum = Rs.(420 x 100/3 x 8) = Rs. 1750.

If the simple interest on a sum of money for 2 years at 5% per annum is Rs. 50, what is the compound interest on the same at the same rate and for the same time?
A. Rs. 51.25
B. Rs. 52
C. Rs. 54.25
D. Rs. 60
Explanation:
Sum = Rs.(50 x 100/2 x 5)= Rs. 500.
Amount = Rs. [500 x (1 + 5/100)2]
= Rs. 500 x 21/20 x 21/20
= Rs. 551.25
C.I. = Rs. (551.25 – 500) = Rs. 51.25

The difference between simple interest and compound on Rs. 1200 for one year at 10% per annul reckoned half-yearly is:
A. Rs. 2.50
B. Rs. 3
C. Rs. 3.75
D. Rs. 4
E. None of these
Explanation:
S.I. = Rs
1200 x 10 x 1/100 = Rs. 120.
C.I. = Rs. [1200 x (1 + 5/100)2 – 1200 = Rs. 123.
Difference = Rs. (123 – 120) = Rs. 3.

The difference between compound interest and simple interest on an amount of Rs. 15,000 for
2 years is Rs. 96. What is the rate of interest per annum?

A. 8
B. 10
C. 12
D. Cannot be determined
E. None of these
Explanation:
[15000 x (1 + R/100)2 – 15000 -] – (15000 x R x 2/100) = 96
15000 [(1 + R/100)2-1 – 2R/100] = 96
15000 [(100 + R)2 – 10000 – (200 x R)/10000] = 96
R2 = (96 x 2/3) = 64
R = 8.
Rate = 8%.

The compound interest on a certain sum for 2 years at 10% per annum is Rs. 525. The simple
interest on the same sum for double the time at half the rate percent per annum is:

A. Rs. 400
B. Rs. 500
C. Rs. 600
D. Rs. 800