The difference between compound interest of three years and simple interest of two years at the rate of 15% p.a. on a certain sum is Rs.176.7/-. Find principal.
Answer & explanation
Correct answer: option 4
15% = \(\frac{3}{20}\)
Now,
S.I for 2 years = 1200 + 1200 = 2400
C.I for 3 years = 3(1200) + 3(180) + 27 = 4167
Difference = 4167 - 2400 = 1767
ATQ,
Difference = 176.7
1767R = 176.7
1R = 0.1
Principal = 8000R = 8000 × 0.1 = 800
OR:
Let the sum = P
Compound interest of three years = P(1 + \(\frac{15}{100}\))3 - P
= P(\(\frac{12167}{8000}\) - 1) = P(\(\frac{4167}{8000}\))
Simple interest of two years = P × \(\frac{15}{100}\) × 2 = \(\frac{3P}{10}\)
Diff. in compound interest of 3 years and S.I. of 2 years = P(\(\frac{4167}{8000}\)) - \(\frac{3P}{10}\) = P(\(\frac{4167 - 2400}{8000}\))
ATQ,
P(\(\frac{1767}{8000}\)) = 176.7
P = 800