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Simple interest

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by cypherskull » Fri May 04, 2012 2:57 pm
Looks like a very simple problem but got an incorrect answer (A).

Shaun invests a certain sum of money at 18.75% p.a. simple interest. After how many years will the sum of money become three times its principal?

A. 16 years

B. 12 years

C. 10 years 8 months

D. 10 years, 6 months, 20 days

E. 10 years 9 months

Ans: C
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by mathbyvemuri » Fri May 04, 2012 6:30 pm
simple interest = 18.75% p.a.
Let the principle = X
Sum after n years = X(1 + 18.75n/100)
The sum is to become three times the principle
=> (1 + 18.75n/100) = 3
=> 18.75n/100 = 3-1 = 2
=> n = 200/18.75 years = 200*12/18.75 months
= 240000/1875 = 80000/625 = 3200/25 = 128 months
= 10 yrs 8 months
it's a calculation based problem
converting years in to months is the key for simpler calculation.
we convert years in to months in order to get 12 in the numerator which is a multiple of 3, which goes evenly in to the denominator 1875, which is also a multiple of 3.
Answer "C"
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by Bill@VeritasPrep » Fri May 04, 2012 7:50 pm
A sum that is three times the principal is also 300% of the principal. This means that we're calculating the time to gain 200% (since we start with 100%)

18.75% * 10 years = 187.5%, leaving 12.5%

12.5/18.75 = 2/3, so we need another 2/3 of a year, or 8 months.

10 years and 8 months.
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