The S.I. and C.I. on a certain sum of money in 2 years with same rate of…

Solution:

Let the principal be p and the annual rate be r%.

• From simple interest for 2 years: (2·p·r)/100 = 1300, so p·r = 65,000.

• Compound interest for 2 years: p[(1 + r/100)^2 − 1] = 1332.5. Expand: p(2r/100 + r^2/10000) = 1332.5.

• Multiply both sides by 10000: p(r^2 + 200r) = 13,325,000.

• Use p·r = 65,000 to rewrite left side as p·r(r + 200) = 65,000(r + 200). So 65,000(r + 200) = 13,325,000.

• Solve for r: r + 200 = 13,325,000 / 65,000 = 205 ⇒ r = 5%.

• Then p = 65,000 / r = 65,000 / 5 = 13,000.

Therefore the sum (principal) is Rs.13,000.