The difference in compound interest on a certain sum at 10 p a for one year when the interest is com...........

Quantitative Aptitude (CGL) Compound Interest

The difference in compound interest on a certain sum at 10% p.a. for one year, when the interest is compounded half yearly

and yearly, is Rs88.80. What is the simple interest on the same sum for $1_{3}^{2}$ years at the same rate?

This questions was previously asked in

SSC CGL 4th March 2020 Shift-2

View All ssc Previous Year Papers

Rs5,916

Rs5,986

Rs5,980

Rs5,920

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Explanation:

Principal = p
Rate(r) = 10%
Time(t) = 1 year
compound interest =p(1 + r/100) t − P
When interest is calculated yearly =p(1 + 10/100) − p = p × (110/100) − p
When interest is calculated half yearly,
Rate(r) = 10/2 = 5%
Time(t) = 1 2 = 2
Interest = $$p(1 + 5/100)^2 - p = p \times (105/100) \times (105/100) - p
Difference of interest = 88.80

p × (105/100) × (105/100) − p − p × (110/100) + p = 88.80
p × 1.05 × 105 − p × 110 = 8880
110.25p - 110p = 8880
p = 8880/.25 = 35520
Simple interest for 1 2/3 years,
t =1 2/3 = 5/3 years
Interest = $$\frac{prt}{100} = \frac{35520 \times 10 \times 5}{100 \times 3}
= Rs.5920

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