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.

Rs. 800

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