At what rate of annual interest will an investment quadruple

At what rate of annual interest will an investment quadruple itself in 12 years? 1.10.1% 2.11.2% 3.12.2% 4.13.1%

Solution

There is no mention of compounding. So we will presume that the rate of interest quoted is simple rate of interest. Let n be the rate of interest at which the amount is quadrupled in 12 years and let the principal (initial amount ) be P . Then the interest on P at r % per annum for 12 years is (P*r /100 )* 12 so that P + (P*r/100 )*12 = 4P or, on dividing both the sides by P, we get 1 +12r/100 = 4 or, 12r/100 = 3 or, 12r = 300 so that r = 300/12= 25%. However, this is nowhere near any of the answers given. Hence, we will attempt the problem again, assuming that the interest is compounded annually.

The formula for compound interest is F = P ( 1 +r )ⁿ where F is the amount on maturity , r is the rate of interest in decimals and n is the number of years. Here, F = 4P, n = 12 . Then 4P = P( 1 + r)¹² or, on dividing both the sides by P, we get 4 = ( 1 + r)¹² or, 1 + r = (4)^1/12 = 1.122462 ( approx) so that r = 0.122462 = 0.122462*199 % = 12.2462 % , say 12.2 % ( on rounding off to 1 decimal place). The 3rd answer is correct.