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- 26. On a sum of money, the simple interest for 2 years is Rs. 320, while the compound interest is Rs. 340, the rate of interest being the same in both the cases. The rate of interest is:
Answer: Option C 
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Solution 1
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Simple interest for 2 years is Rs. 320
=> Simple interest for first year = 320/2 = 160
=> Similarly, simple interest for second year is also 160
Compound Interest for first year = 160
Compound Interest for second year = 340-160 = 180
we can see that compound Interest for second year is more than
simple interest for second year by 180-160 = 20
i.e., Rs.20 is the simple interest on Rs.160 for 1 year
R = 100 × SI/PT = (100 × 20)/(160 × 1) = 12.5%
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Solution 2
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= (R × SI)/(2 × 100)
Difference between the compound interest and simple interest = 340 - 320 = 20
(R × SI)/(2 × 100) = 20
(R × 320)/(2 × 100) = 20
R = 20 × 100 × 2320 = 12.5%
View Answer
- 27. A bank offers 10% interest rate compounded annually. A person deposits Rs. 20,000 every year in his account. If he does not withdraw any amount, then how much balance will his account show after four years?
Answer: Option A
Rs.20000 after 4 years = 20000(1+10/100)4 = 20000(11/10)4 = Rs. 29282
Rs.20000 after 3 years = 20000(1+10/100)3 = 20000(11/10)3 = Rs. 26620
Rs.20000 after 2 years = 20000(1+10/100)2 = 20000(11/10)2 = Rs. 24200
Rs.20000 after 1 year = 20000(1+10/100)1 = 20000(11/10) = Rs. 22000
Total amount after 4 years = 29282 + 26620 + 24200 + 22000 = Rs. 102102
View Answer
- 28. A sum of money becomes Rs. 2200 after three years and Rs. 4400 after six years on compound interest. The sum is
Answer: Option B
Let the sum be P and rate of interest be R% per annum.
Amount after 3 years = 2200
P(1 + R/100)T = 2200
P(1 + R/100)3 = 2200 --- ( 1)
Amount after 6 years = 4400
P(1+R/100)T = 4400
P(1 + R/100)6 = 4400 --- (2)
(2) ÷ (1) => [P(1+R/100)6]/[P(1+R/100)3] = 4400/2200 = 2
=> (1+R/100)3 = 2 (Substituting this value in equation 1)
=> P × 2 = 2200
P = 22002 = 1100
View Answer
- 29. What annual payment will discharge a debt of Rs. 1025 due in 2 years at the rate of 5% compound interest?
Answer: Option C
Present worth of Rs. x due T years hence is given by
Present Worth (PW) = x/(1+R/100)T
Let x be the annual payment
Then, present worth of x due 1 year hence + present worth of x due 2 year hence = 1025
x(1 + 5/100)1 + x(1 + 5/100)2 = 1025 x/(21/20) + x/(21/20)2 = 1025
20x/21 + 400x/441 = 1025
820x/441 = 1025
x = (1025 × 441)/820
= (205 × 441)/164
= Rs. 551.25
View Answer
- 30. If the compound interest on a certain sum for 2 years in Rs. 80.80 and the simple interest Rs. 80; then the rate of interest per annum is
Answer: Option A
Let the sum be P and Rate of Interest be R% per annum
Simple Interest on Rs.P for 2 years = 80
PRT/100 = 80
(PR × 2)/100 = 80
PR/50 = 80
PR = 4000 - -- (equation 1)
Compound Interest = P(1 + R/100)T - P
= P(1 + R/100)2 - P
= P[(1 + R/100)2 - 1] = P[(1 + 2R/100 + R2/10000) - 1] = P(2R/100 + R2/10000)
= 2PR/100 + PR2/10000
= 2PR/100 + (PR × R)/10000
= [2 × 4000]/100 + (4000 × R)/10000 ( substituted the value of PR from equation 1)
= 80 + 0.4R
Given that compound interest = Rs.80.80
=> 80 + 0.4R = 80.80
=> 0.4R = 0.80
=> R = 0.80/0.4 = 2%
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