Problems on Simple and Compound Interest-RRB

Interest-RRB Problems on Simple and Compound Interest-RRB

Simple and Compound Interest

Question 1

If a sum of Rs.8000 lended for 20% per annum at compound interest then the sum of the amount will be Rs.13824 in:

a) 2 years b) 1year c) 3years d) 4years

Answer : c)3years

Solution :

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

When interest is compounded Annually total amount can be calculated by using the formula,
Total Amount = P(1 + R/100)ⁿ

Given that, P = Rs.8000, R = 20% per annum
We have to find the time period during which the amount will be Rs.13824

i.e., Rs.13824 = 8000 x (1 + 20/100)^n
13824/8000 = (120/100)ⁿ
(24/20)^3 = (12/10)ⁿ
(12/10)^3 = (12/10)ⁿ
Therefore, n = 3.
Hence the required time period is 3 years.

Question 2

Find the compound interest on a principal amount of Rs.5000 after 2 years, if the rate of interest for the 1st year is 2% and for the 2nd year is 4%.

a) Rs.304 b) Rs.314 c) Rs.324 d) Rs.334

Answer : a)Rs.304

Solution :

When Rates are different for different years, say R1%, R2%, R3% for 1st, 2nd and 3rd year respectively.
Then, Amount (= Principal + Compound interest) = P(1 + R1/100)(1 + R2/100)(1 + R3/100).
Here R1 = 2% R2 = 4% and p = Rs.5000, we have to find CI (compound interest).
CI = 5000(1 + 2/100)(1 + 4/100) – 5000
= 5000 x (102/100)(104/100) – 5000
= 5000 x (51/50) x (52/50) – 5000
= 5000 x (51 x 52/2500) – 5000
= 5000 x (2652 / 2500) – 5000
= 5304 – 5000 = 304
Hence the required compound interest is Rs.304.

Question 3

What sum(principal) will be amount to Rs.34536.39 at compound interest in 3 years, the rate of interest for 1st, 2nd and 3rd year being 5%, 6% and 7% respectively?

a) Rs.25576 b) Rs.29000 c) Rs.28012 d) Rs.24000

Answer : b)Rs.29000

Solution :

Let Rs.P be the required sum.
34536.39 = p(1 + 5/100)(1 + 6/100)(1 + 7/100)
= p (105/100) x (106/100) x (107/100)
p = 34536.39 x 100 x 100 x 100 / 105 x 106 x 107
p = Rs.29000
Hence the required amount is Rs.29000

Question 4

What will be the amount if sum of Rs.10,00,000 is invested at compound interest for 3 years with rate of interest 11%, 12% and 13% respectively?

a) Rs.14,04,816 b) Rs.12,14,816 c) Rs.11,35,816 d) Rs.16,00,816

Answer : a)Rs.14,04,816

Solution:

Here, P = Rs.10,00,000 R1 = 11 R2 = 12 R3 = 13.
Therefore, Amount after 3 years
= p(1 + R1/100)(1 + R2/100)(1 + R3/100)
= 10,00,000 x(1 + 11/100)x(1 + 12/100)x(1 + 13/100)
= 10,00,000 x (111/100) x (112/100) x (113/100)
= 111 x 112 x 113
= 1404816
Hence the total amount after 3 years is Rs.14,04,816.

Question 5

A man lent out Rs.9600 at 9/2 % per annum for a year and 9 months. At the end of the duration, the amount he earned as S.I was:

a) Rs. 567 b) Rs.756 c) Rs.874 d) Rs.784

Answer :b) Rs.756

Solution :
Given that, principal = P = Rs.9600, R = 9/2 % and T = 1 year and 9 months = 1 + 9/12 year = 7/4 years.
Now, we have to find the S.I for 7/4 years.
S.I = PRT/100 = Rs. 9600 x 9/2 x 7/4 x 1/100 = 12 x 9 x 7 = 756
Hence, the required S.I amount is Rs.756

Question 6

A man borrowed Rs.33600 at 25/4 % per annum on September 2012 and he paid back in May 2013. Find the amount he paid as S.I.

a) Rs.2075 b) Rs.2575 c) Rs.1575 d) Rs.1975

Answer : c) Rs.1575.

Solution :
Given that, principal = P = Rs. 33600 and R = 25/4 %.
Time duration = From September 2012 to May 2013 = 9 months = 9/12 year = 3/4 year.
S.I = PRT/100 = Rs. 33600 x 25/4 x 3/4 x 1/100 = 21 x 25 x 3 = Rs.1575.
Hence, the answer is Rs.1575.

Question 7

How much time will it take for a sum of Rs. 9000 to yield Rs. 1620 as S.I at 4 1/2 % per annum?

a) 1 year b) 2 years c) 3 years d) 4 years

Answer :d) 4years.

Solution :

Given that, Principal = P = Rs. 9000, S.I = Rs. 1620 and rate R = 4 1/2 % = 9/2 %
We have to find T.
T = S.I x 100/PR = 1620 x 100/9000 x (9/2)
= 162×2 / 9×9 = 4
Therefore, required time is 4 years.

Question 8

At what rate of simple interest, a sum of Rs.8540 amounts to Rs.9710 in 3 years?

a) 3 1/2 % b) 2 1/4 % c) 3 3/4 % d) 4 1/2 %

Answer : d) 4 1/2 %

Solution :

Given that, principal = P = Rs. 8540
Final amount = Rs. 9710
Then, interest = S.I = Rs.9710 – Rs.8540 = Rs. 1170.
Time = T = 3 years.
Required rate = R = S.I x 100 / PxT = 1170 x 100 / 8540 x 3 = 1950/427
= 4.566 = 4.5 (approximately) = 9/2 = 4 1/2 %
Hence, the answer is 4 1/2 %.

Find the simple interest on Rs. 5000 at a certain rate if the compound interest on the same amount for 2 years is Rs. 253.125.

Solution:

Let the rate of interest be r.

5000[1+ r/100]² = 5000+253.125

→ [1+r/100]² = 5253.125/5000

Solving which gives

[1+ r/100]² = 1681/1600

→ 1+r/100 = 41/40

→ r = 2.5

Therefore, SI = 5000× 2 × 2.5/ 100 = Rs. 250.

Question 10

On a sum of money, the simple interest for 2 years is Rs.660, while the compound interest is Rs.696.30, the rate of interest being the same in both the cases. The rate of interest is :

a) 10% b) 10.5% c) 12% d) Data inadequate e) None of these

Solution:

Answer is Option e

Difference in C.I. and S.I. for 2 years – Rs. (696.30 ⎯ 660) = Rs.36.30

S.I. for one year = Rs.330

Question 11

The difference between the compound interest and simple interest on a certain sum at 12% per annum for 2 years is Rs.700. Find the sum.

Solution:

assuming principal to be X.
we know that N = 2 years, R = 12%

Let us start with Compound Interest:
applying P = X, N = 2 and R = 12 in compound interest formula as shown below:
CI = [P(1 + R/100)ⁿ] – P
= (X[1 + 12/100]²) – X
= (X[112/100]²) – X
= (X[28/25 x 28/25] ) – X
CI = 159X / 625 ………….. equation 1

Now moving on to Simple Interest
substitute P = X, N = 2 and R = 12 in simple interest formula.
SI = PNR/100
= (X x 2 x 12) / 100
= 24X/100
SI = 12X/50 … ……………….equation 2

Now find P
from the question , difference between simple and compound interests is 700
Therefore,
CI – SI = 700 (We are writing CI first because CI will be higher than SI same rate of interest and same number of years)

If you substitute CI and SI values from equations 1 and 2, you will get
159X/625 – 12X/50 = 700
(318X – 300X)/1250 = 700
18X/1250 = 700
700 x 1250 = 18X
Or, X = 48611.11
Principal (Sum invested) = Rs.48611.11

Question 12

If the simple interest on a sum of money at 6% per annum for 4 years is Rs.1600, then find the compound interest on the same sum for the same period at the same rate.

Solution:
From the question, you know that R = 6%, N = 4 years, SI = Rs.1600

If you apply the above values in the simple interest formula SI = PNR/100, you will get
1600 = P x 4 x 6 / 100
Or P = (1600 x 100) / 6 x 4
P = 6333.33

Using the above value of P, you have to now calculate CI as shown below:
CI = [P(1 + R/100)ⁿ] – P
= [6333.33(1 + 6/100)⁴] – 6333.33
= [6333.33 (106/100)⁴] – 6333.33
= [6333.33 x 53/50 x 53/50 x 53/50 x 53/50] – 6333.33
= 7995.68 – 6333.33
= Rs.1662.35

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