A sum of ₹7500 amounts to ₹9075 at 10% p.a, interest being compounded yearly in a certain time. The simple interest (in ₹) on the same sum for the same time and the same rate is:
Answer & explanation
Correct answer: option 1
7500 becomes 9075 at 10% per annum at Compound interest
A=P(1+\(\frac{R}{100}\))T
where A = Amount , P = Principal, R = Rate and T = Time
So,
9075=7500(1+\(\frac{10}{100}\))T
\(\frac{9075}{7500}\)=(\(\frac{11}{10}\))t
\(\frac{121}{100}\)=(\(\frac{11}{10}\))t
(\(\frac{11}{10}\))2 =(\(\frac{11}{10}\))t
∴ T = 2 years
Now
P = 7500
R = 10%
T = 2 years
Simple Interest = \(\frac{P×R×T}{100}\)
S.I. = \(\frac{7500×10×2}{100}\)
S.I. = Rs 1500