at what rate percent simple interest will a sum of money triple itself in 6 years
Answers
Calculating simple interest is quiet easy. Assuming you initially have 100 dollars.
100 (1 + r*T) = 200 (since the amount needs to get doubled)
Here r = simple interest rate and ‘T’ is number of time periods. If ‘r’ is in interest per quarter then ‘T’ is in number of quarters. If ‘r’ is in interest per year then ‘T’ is in number of years. For now lets assume that ‘r’ is in interest per year. That makes T=8 according to your question. Solving the above equation:
1 + r*8 = 2 (dividing with 100 on both sides)
r=.125 or 12.5%
Most of the real world works on a compound interest basis and not on simple interest basis. For example bank deposits. What is mean by this is that if you earn a interest in the current period, in the next period you will not only earn interest on the principal but also on the interest you earned in the last period. In mathematical terms
100*(1+r/n)^nT = 200
where n= frequency of compounding or the number of times the interest in declared in a year. Assuming half yearly compounding,
(1+r/2)^2*8 = 2
r = 0.08854 or 8.85%
However calculating 2^(1/16) is very complicated and you will a calculator. If you are looking for a quick and rough estimate you can use the 72 rule. This is how 72 rule works : r * T = 72 where T is in years and r is compounded annual interest rate.
In the above case T=8. from 72 rule that implies r = 72/8 = 9% which is pretty close to our actual estimate 8.85%
Answer
Let principal be = x
Amount = 3x
Simple Interest = Amount - principal
= 2x
Time = 6 years
SI = PRT/100
2x = 6Rx/100
R = 200/6