If the simple interest on sum of money for 2 years at 10% per
annum is Rs. 3750. Then what will be the compound interest on
same sum at the same rate for the same period, compounded
annually.
Answers
Step-by-step explanation:
S.I=Rs.340,Time=2 years,R=4%
(i)Let the sum of money be rs.x
S.I=
100
PRT
⇒340=
100
x×4×2
⇒x=
4×2
340×100
=Rs.4250
(ii)C.I for Rs. 4250 for one year payable half-yearly
∴ T=1 year=2 half year,Rate=
2
4
=2%
A=P(1+
100
R
)
T
⇒4250(1+
100
2
)
2
⇒4250(
100
102
)
2
⇒4250×
50
51
×
50
51
=4421.70
C.I=A−P
⇒4421.70−4250=Rs.171.70
Step-by-step explanation:
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Question Download Soln PDF
A sum of money is invested for 2 years at 10% compound interest p.a. It would fetch Rs. 1,762 more if interest is calculated half yearly. Find the sum invested.
This question was previously asked in
NTPC CBT-I (Held On: 30 Dec 2020 Shift 2)
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Rs. 2,30,000Rs. 3,40,000Rs. 3,30,000Rs. 3, 20,000
Answer (Detailed Solution Below)
Option 4 : Rs. 3, 20,000
Detailed Solution Download Soln PDF
Given:
Difference between the compound interest received for 2 years compounded annually and half yearly = Rs.1762
Time = 2 years
Rate = 10% per annum
Formulas used:
Compound Interest = Amount - Principal
⇒ Amount = Principal + Compound Interest
⇒ Amount = Principal × (1 + r/100)n [n = No of periods]
Calculation:
Amount, when interest is compounded annually:
n = 2, R = 10%
⇒ P (1 + 10/100)2
⇒ P (11/10)2 (1)
Amount, when interest is compounded half yearly:
n = 2 × 2 = 4
Rate = 10%/2 = 5%
⇒ P (1 + 5/100)4
⇒ P (105/100)4
⇒ P (21/20)4 (2)
As per the question:
P (21/20)4 - P (11/10)2 = 1762
⇒ P (21 × 21 × 21 × 21) ÷ (20 × 20 × 20 × 20) - P (11 × 11) ÷ (10 × 10) = 1762
⇒ P [194481/160000 - 121/100] = 1762
⇒ P [(194481 - 1600 × 121)/160000] = 1762
⇒ P [(194481 - 193600)/160000] = 1762
⇒ P [881/160000] = 1762
⇒ P × 881 = 1762 × 160000
⇒ P = (1762 × 160000)/881
⇒ P = 320000
∴ The required sum is Rs.320000.