What is the difference between the compound interests on Rs.5000 for 1.5 years at 4% per annum compounded yearly and half-yearly?
- Rs. 3.21
- Rs. 2.37
- Rs. 3.45
- Rs. 2.04
- Rs. 3.60
Answer [Detailed Solution Below]
Option 4 : Rs. 2.04
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As we know that:-
The formula for annual compound interest, including principal sum, is:
A = P [1 + r/n] [nt]
Where: A = the future value of the investment/loan, including interest
P = the principal investment amount [the initial deposit or loan amount]
r = the annual interest rate [decimal]
n = the number of times that interest is compounded per year
t = the number of years the money is invested or borrowed for
C.I. when interest compounded yearly = Rs. 5000 × [1 + 4/100] × [1 + [4/2] /100]
= Rs.[5000 × 26/25 × 51/50] = Rs. 5304.
C.I. when interest is compounded half-yearly = Rs. 5000 × [1 + 2/100] 3
= Rs.[5000 × 51/50 × 51/50 × 51/50] = Rs. 5306.04
Difference = Rs.[5306.04 - 5304] = Rs. 2.04
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Solution
The correct option is C
₹ 1655
Given:
P = ₹ 5000
R = 20% per annum, so will be 10% when compounded half-yearly
n = 3 [As 1.5 years has 3 half years in it]
Compound interest will be calculated by C.I
= [P×[1+R100]n]−P
Substituting the values, we get,
C.I=[5000 × [1+10100]3]−5000
C.I=[5000×1110×1110×1110]−5000
C.I=₹ 6655−₹5000
C.I=₹ 1655