relation among principal, time, rate percent of Interest per annum and total Interest Suppose, Principal = P, Time = t years, Rate of interest per annum = r% and Total interest = I Then I = P x R x T / 100
i.e. Total interest = PrincipalT imeR ateofinterestperannum 100 ¥¥ Since the Amount = Principal + Total interest.
1. The SI on a sum of money is 25% of the principal, and the rate per annum is equal to the number of years. Find the rate percent. (a) 4.5% (b) 6% (c) 5% (d) 8%
Let principal = x, time = t years Then interest = x/4, rate = t% Now, using the SI formula, we get Interest = (Principal ¥ Rate ¥ Time)/100 fi x/4 = (x X t X t)/100 = t^2 = 25 fi t = 5%.
2. The rate of interest for fi rst 3 years is 6% per annum, for the next 4 years, 7 per cent per annum and for the period beyond 7 years, 7.5 percentages per annum. If a man lent out 1200 for 11 years, fi nd the total interest earned by him? (a) 1002 (b) 912 (c) 864 (d) ` 948
Whenever it is not mentioned whether we have to assume SI or CI we should assume SI. For any amount, interest for the 1st three years @ 6% SI will be equal to 6 ¥ 3 = 18% Again, interest for next 4 years will be equal to 7 ¥ 4 = 28%. (daveseminara.com) And interest for next 4 years (till 11 years) –7.5 X 4 = 30% So, total interest = 18 + 28 + 30 = 76% So, total interest earned by him = 76% of the amount = () 76 X 1200 / 100 = ` 912 This calculation can be done very conveniently using the percentage rule as 75% + 1% = 900 + 12 = 912.