RD Sharma Class 8 Solutions Chapter 14 Compound Interest Ex 14.3



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TextbookNCERT
ClassClass 8
SubjectMaths
ChapterChapter 14
Chapter NameCompound Interest
ExerciseEx 14.3

RD Sharma Solutions for Class 8 Chapter 14 Compound Interest Ex 14.3 Download PDF

Question 1.
On what sum will the compound interest at 5% p.a. annum for 2 years compounded annually be Rs 164 ?
Solution:
Let Principal (P) = Rs 100
Rate (R) = 5% p.a.
Period (n) = 2 years
RD Sharma Class 8 Solutions Chapter 14 Compound Interest Ex 14.3 1
RD Sharma Class 8 Solutions Chapter 14 Compound Interest Ex 14.3 2

Question 2.
Find the principal of the interest compounded annually at the rate of 10% for two years is Rs 210.
Solution:
Let principal (P) = Rs 100
Rate (R) = 10% p.a.
Period (n) = 2 years
RD Sharma Class 8 Solutions Chapter 14 Compound Interest Ex 14.3 3
RD Sharma Class 8 Solutions Chapter 14 Compound Interest Ex 14.3 4

Question 3.
A sum amounts to Rs 756.25 at 10% per annum in 2 years, compounded annually. Find the sum.
Solution:
Amount (A) = Rs 756.25
Rate (R) = 10% p.a.
Period (n) = 2 years
RD Sharma Class 8 Solutions Chapter 14 Compound Interest Ex 14.3 5

Question 4.
What sum will amount to Rs 4913 in 18 months, if the rate of interest is 1212 % per annum, compounded half-yearly.
Solution:
Amount (A) = Rs 4,913
RD Sharma Class 8 Solutions Chapter 14 Compound Interest Ex 14.3 6

Question 5.
The difference between the compound interest and simple interest on a certain sum at 15% per annum for 3 years is Rs 283.50. Find the sum.
Solution:
Let sum (P) = Rs 100
Rate (R) = 15% p.a.
Period (n) = 3 years
RD Sharma Class 8 Solutions Chapter 14 Compound Interest Ex 14.3 7
RD Sharma Class 8 Solutions Chapter 14 Compound Interest Ex 14.3 8
RD Sharma Class 8 Solutions Chapter 14 Compound Interest Ex 14.3 9

Question 6.
Rachna borrowed a certain sum at the rate of 15% per annum. If she paid at the end of two years Rs 1,290 as interest compounded annually, find the sum she borrowed.
Solution:
C.I. = Rs 1,290
Rate (R) = 15% p.a.
Period (n) = 2 years
Let sum (P) = Rs 100
RD Sharma Class 8 Solutions Chapter 14 Compound Interest Ex 14.3 10

Question 7.
The interest on a sum of Rs 2,000 is being compounded annually at the rate of 4% per annum. Find the period for which the compound interest is Rs 163.20.
Solution:
Sum (P) = Rs 2,000
C.I. = Rs 163.20
Amount (A) = P + C.I. = Rs 2000 + Rs 163.20 = Rs 2163.20
Rate (R) = 4%
Let period = n years
RD Sharma Class 8 Solutions Chapter 14 Compound Interest Ex 14.3 11
RD Sharma Class 8 Solutions Chapter 14 Compound Interest Ex 14.3 12

Question 8.
In how much time would Rs 5,000 amount to Rs 6,655 at 10% per annum compound interest ?
Solution:
Principal (P) = Rs 5,000
Amount (A) = Rs 6,655
Rate (R) = 10%
Let period = n years.
RD Sharma Class 8 Solutions Chapter 14 Compound Interest Ex 14.3 13

Question 9.
In what time will Rs 4,400 becomes Rs 4,576 at 8% per annum interest compounded half-yearly ?
Solution:
Principal (P) = Rs 4,400
Amount (A) = Rs 4,576
Rate (R) = 8% or 4% half-yearly
Let period = n half-years
RD Sharma Class 8 Solutions Chapter 14 Compound Interest Ex 14.3 14
n = 1
Period = 1 half year

Question 10.
The difference between the S.I. and C.I. on a certain sum of money for 2 years at 4% per annum is Rs 20. Find the sum.
Solution:
Difference between C.I. and S.I. = Rs 20
Rate (R) = 4% p.a.
Period (n) = 2 years
Let principal (P) = Rs 100
RD Sharma Class 8 Solutions Chapter 14 Compound Interest Ex 14.3 15
RD Sharma Class 8 Solutions Chapter 14 Compound Interest Ex 14.3 16

Question 11.
In what time will Rs 1,000 amount to Rs 1,331 at 10% per annum compound interest.
Solution:
Principal (P) = Rs 1,000
Amount (A) = Rs 1,331
Rate (R) = 10% p.a.
Let period = n year
lass 8 Solutions Chapter 14 Compound Interest Ex 14.3 17

Question 12.
At what rate percent compound interest per annum will Rs 640 amount to Rs 774.40 in 2 years ?
Solution:
Principal (P) = Rs 640
Amount (A) = Rs 774.40
Period (n) = 2 years.
Let R be the rate of interest p.a.
lass 8 Solutions Chapter 14 Compound Interest Ex 14.3 18
lass 8 Solutions Chapter 14 Compound Interest Ex 14.3 19

Question 13.
Find the rate percent per annum if Rs 2000 amount to Rs 2,662 in 112 years, interest being compounded half-yearly ?
Solution:
Principal (P) = Rs 2,000
Amount (A) = Rs 2,662
lass 8 Solutions Chapter 14 Compound Interest Ex 14.3 20

Question 14.
Kamala borrowed from Ratan a certain rate for two years simple interest. She lent this sum at the same rate to Hari for two years compound interest. At the end of two years, she received Rs 210 as compound interest, but paid Rs 200 only as simple interest. Find the sum and the rate of interest.
Solution:
Simple interest = Rs 200
and compound interest = Rs 210.
Period = 2 years
lass 8 Solutions Chapter 14 Compound Interest Ex 14.3 21

Question 15.
Find the rate percent per annum, if Rs 2,000 amount to Rs 2,315.25, in an year and a half, interest being compounded six monthly.
Solution:
Principal (P) = Rs 2,000
Amount (A) = Rs 2315.25
lass 8 Solutions Chapter 14 Compound Interest Ex 14.3 22
lass 8 Solutions Chapter 14 Compound Interest Ex 14.3 23

Question 16.
Find the rate at which a sum of money will double itself in 3 years, if the interest is compounded annually.
Solution:
Let Principal (P) = Rs 100
then Amount (A) = Rs 200
Period (n) = 3 years
Let R be the rate % p.a.
lass 8 Solutions Chapter 14 Compound Interest Ex 14.3 24

Question 17.
Find the rate at which a sum of money will become four times the original amount in 2 years, if the interest is compounded half- yearly.
Solution:
Let Principal (P) = Rs 100
Then Amount (A) = Rs 400
Period (n) = 2 years or 4 half years
Let R be the rate % half-yearly, then
lass 8 Solutions Chapter 14 Compound Interest Ex 14.3 25
Rate % = 41.42% half yearly and 82.84% p.a.

Question 18.
A certain sum amounts to Rs 5,832 in 2 years at 8% compounded interest. Find the sum.
Solution:
Amount (A) = Rs 5,832
Let P be the sum
Rate (R) = 8% p.a.
Period (n) = 2 years
lass 8 Solutions Chapter 14 Compound Interest Ex 14.3 26

Question 19.
The difference between the compound interest and simple interest on a certain sum for 2 years at 7.5% per annum is Rs 360. Find the sum.
Solution:
Let sum (P) = Rs 100
lass 8 Solutions Chapter 14 Compound Interest Ex 14.3 27
lass 8 Solutions Chapter 14 Compound Interest Ex 14.3 28

Question 20.
The difference in simple interest and compound interest on a certain sum of money at 623 % per annum for 3 years is Rs 46. Determine the sum.
Solution:
Let sum (P) = Rs 100
lass 8 Solutions Chapter 14 Compound Interest Ex 14.3 29
lass 8 Solutions Chapter 14 Compound Interest Ex 14.3 30
lass 8 Solutions Chapter 14 Compound Interest Ex 14.3 31

Question 21.
Ishita invested a sum of Rs 12,000 at 5% per annum compound interest. She received an amount of Rs 13,230 after n years, Find the value of n.
Solution:
Principal (P) = Rs 12,000
Amount (A) = Rs 13,230
Rate (R) = 5% p.a.
Period = n years
lass 8 Solutions Chapter 14 Compound Interest Ex 14.3 32

Question 22.
At what rate percent per annum will a sum of Rs 4,000 yield compound interest of Rs 410 in 2 years ?
Solution:
Principal (P) = Rs 4,060
C.I. = Rs 410
Amount (A) = Rs 4,000 + 410 = Rs 4,410
Let rate = R % p.a.
Period (n) = 2 years
lass 8 Solutions Chapter 14 Compound Interest Ex 14.3 33

Question 23.
A sum of money deposited at 2% per annum compounded annually becomes Rs 10404 at the end of 2 years. Find the sum deposited.
Solution:
Amount (A) = Rs 10,404
Rate (R) = 2% p.a.
Period (n) = 2 years.
RD Sharma Class 8 Solutions Chapter 14 Compound Interest Ex 14.3 18
RD Sharma Class 8 Solutions Chapter 14 Compound Interest Ex 14.3 19

Question 24.
In how much time will a sum of Rs 1,600 amount to Rs 1852.20 at 5% per annum compound interest ?
Solution:
Principal (P) = Rs 1,600
Amount (A) = Rs 1852.20
Rate (R) = 5% p.a.
Let n be the time
RD Sharma Class 8 Solutions Chapter 14 Compound Interest Ex 14.3 20

Question 25.
At what rate percent will a sum of Rs 1,000 amount to Rs 1102.50 in 2 years at compound interest ?
Solution:
Principal (P) = Rs 1,000
Amount (A) = Rs 1102.50 .
Period (n) = 2 years
Let R be the rate of interest p.a.
RD Sharma Class 8 Solutions Chapter 14 Compound Interest Ex 14.3 21

Question 26.
The compound interest on Rs 1,800 at 10% per annum for a certain period of time is Rs 378. Find the time in years.
Solution:
Principal (P) = Rs 1,800
C.I. = Rs 378
Amount (A) = P + C.I. = Rs 1,800 + 378 = Rs 2,178
Rate (R) = 10% p.a.
Let n be the period in years
RD Sharma Class 8 Solutions Chapter 14 Compound Interest Ex 14.3 22
Comparing, we get:
n = 2
Period = 2 years

Question 27.
What sum of money will amount to Rs 45582.25 at 634 % per annum in two years, interest being compounded annually ?
Solution:
Amount (A) = Rs 45582.25
RD Sharma Class 8 Solutions Chapter 14 Compound Interest Ex 14.3 23

Question 28.
Sum of money amounts to Rs 4,53,690 in 2 years at 6.5% per annum compounded annually. Find the sum.
Solution:
Amount (A) = Rs 4,53,690
RD Sharma Class 8 Solutions Chapter 14 Compound Interest Ex 14.3 24
RD Sharma Class 8 Solutions Chapter 14 Compound Interest Ex 14.3 25
RD Sharma Class 8 Solutions Chapter 14 Compound Interest Ex 14.3 26

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