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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
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A. Rs. 51.25
B. Rs. 52
C. Rs. 54.25
D. Rs. 60
E. None of these
Solution(By Examveda Team)
$$\eqalign{ & {\text{Sum}} = Rs.\,\left( {\frac{{50 \times 100}}{{2 \times 5}}} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\, = Rs.\,500 \cr & {\text{Amount}} = Rs.\,\left[ {500 \times {{\left( {1 + \frac{5}{{100}}} \right)}^2}} \right] \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = Rs.\,\left( {500 \times \frac{{21}}{{20}} \times \frac{{21}}{{20}}} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = Rs.\,551.25 \cr & \therefore {\text{C}}{\text{.I}}{\text{.}} = Rs.\,\left( {551.25 - 500} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = Rs.\,51.25 \cr} $$
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 sum at the same rate and for the same time?
- Rs. 51.25
- Rs. 52
- Rs. 54.25
- Rs. 60
Answer (Detailed Solution Below)
Option 1 : Rs. 51.25
Free
15 Questions 15 Marks 13 Mins
Given:
Time = 2 years
Rate of interest = 5%
S.I. = Rs. 50
Calculation:
S.I. = PRT/100
⇒ 50 = P × 5 × 2/100
⇒ 5 = P/100
⇒ P = 500
A = P[1 + (r/100)]t
⇒ A = 500[1 + (5/100)]2
⇒ A = 500 × (21/20) × (21/20)
⇒ A = 551.25
C.I. for 2 years = 551.25 - 500 = Rs. 51.25
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Stay updated with the Quantitative Aptitude questions & answers with Testbook. Know more about Interest and ace the concept of Simple Interest.
If the simple interest on a sum of money for 2 yr at 5% per annum is Rs. 50, what is the compound interest on the same at the same rate and for the same time?
- Rs. 51.25
- Rs. 52
- Rs. 54.25
- Rs. 60
Answer (Detailed Solution Below)
Option 1 : Rs. 51.25
Free
CT 1: International and National Awards
10 Questions 10 Marks 8 Mins
Given :
S.I on money for 2 year at 5% = Rs. 50
Formula used :
S.I. = P × R × T / 100
Amount (A) = P(1 + R/100)n
C.I = A - P
Where,
P = principal, R= Rate, T= Time
Calculation :
We know that
S.I. = P × R × T / 100
50 = P × 5 × 2 /100
⇒ P = 500
Again, in compound interest, the amount
⇒ A = 500(1 + 5/100)2
⇒ A = 500 (1 + .05)2
⇒ A = Rs. 551.25
Hence, compound interest
C.I = 551.25 - 500 = Rs. 51.25
∴ Compound Interest = Rs. 51.25
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