If an amount is kept at Simple Interest, it earns Rs.600 in first 2 years but when kept at Compound Interest it earns at interest of Rs.660 for the same period; then the rate of interest and principle amount respectively are:
(a) 20%; Rs.1200 (b) 10%; Rs.1200 (c) 20%; Rs.1500 (d) 10%; Rs.1500
Answers
If an amount is kept at Simple Interest, it earns Rs.600 in first 2 years but when kept at Compound Interest it earns at interest of Rs.660 for the same period.
To find : rate of interest and principal amount respectively.
solution : let the rate of interest is r % per annum and P is the principal amount.
case 1 : S.I = P × r × t/100
⇒Rs. 600 = P × r × 2/100
⇒Pr = 30000 .......(1)
case 2 : C.I = P(1 + r/100)ⁿ - P
⇒Rs. 660 = P[(1 + r/100)² - 1]
⇒660 = P[1 + r²/10000 + r/50 - 1 ]
⇒660 = Pr/50 + Pr²/10000
⇒660 = Pr/50(1 + r/200)
⇒33000 = Pr(1 + r/200).......(2)
from equations (1) and (2) we get,
30000/33000 = 1/(1 + r/200)
⇒1/1.1 = 1/(1 + r/200)
⇒1.1 = 1 + r/200
⇒0.1 = r/200
⇒r = 20 %
now, Pr = 30000
⇒P × 20 = 30000
⇒P = 1500
Therefore the rate of interest is 20% and principal amount is 1500. so option (c) is correct choice.