SOLUTION: How long will it take a sum of money to double itself if interest 12(1/2)% per annum

Question 1202792: How long will it take a sum of money to double itself if interest 12(1/2)% per annum
Found 4 solutions by mananth, ikleyn, math_tutor2020, greenestamps:
Answer by mananth(16946)   (Show Source): You can put this solution on YOUR website!

Let Principal be P
doubles in how many years =2P
Interest = 2P-P=P
Rate = 12.5% = 0.125
I = P * n*r
P = P*n *0.125
n= 1/0.125
= 8 years

Answer by ikleyn(52812)   (Show Source): You can put this solution on YOUR website!
.
How long will it take a sum of money to double itself if interest 12(1/2)% per annum
~~~~~~~~~~~~~~~~~~~

As the problem is worded, printed, posted and presented, it is FATALLY INCOMPLETE.

To be complete, it MUST say if the account is simple interest or a compound interest.

From the distance of thousands miles, it is clearly seen that the person who created it,
is unfamiliar with standard formulations of this type of problems.

Answer by math_tutor2020(3817)   (Show Source): You can put this solution on YOUR website!

12 & 1/2 = 12.5
12.5% = 0.125 in decimal form

If you're working with simple interest, then,
A = P*(1+r*t)
2P = P*(1+0.125*t)
2 = 1+0.125*t
1+0.125*t = 2
0.125*t = 2-1
0.125*t = 1
t = 1/0.125
t = 8
It will take 8 years for the money to double at 12.5% simple interest.

If you're working with compound interest, when the money is compounded annually, then,
A = P*(1+r/n)^(n*t)
2P = P*(1+0.125/1)^(1*t)
2 = (1.125)^t
log(2) = log( (1.125)^t )
log(2) = t*log(1.125)
t = log(2)/log(1.125)
t = 5.88494919236171
t = 5.8849
It will take about 5.8849 years for the money to double at 12.5% compound interest, when the money is compounded annually.

If you're working with compound interest, when the money is compounded semi-annually, then,
A = P*(1+r/n)^(n*t)
2P = P*(1+0.125/2)^(2*t)
2 = (1.0625)^(2t)
log(2) = log( (1.0625)^(2t) )
log(2) = 2t*log(1.0625)
t = log(2)/(2*log(1.0625))
t = 5.71671343912647
t = 5.7167
It will take about 5.7167 years for the money to double at 12.5% compound interest, when the money is compounded semi-annually.

I'll skip the steps for other cases of n, but you should get these approximate time values.

N T
1 5.8849
2 5.7167
4 5.6314
12 5.5740
365 5.5461

Answer by greenestamps(13203)   (Show Source): You can put this solution on YOUR website!

Since the reader has posted other similar questions specifying simple interest, I assume this problem is also with simple interest....

With simple interest, this can be solved using common sense and basic arithmetic; no mathematical formulas are needed.

With simple interest, 12.5% of the original amount is added each year.
For the original amount to double, 100% has to be added to the original amount.
The number of years required to add 100% to the original amount, at 12.5% per year, is 100/12.5 = 8.

ANSWER: 8 years

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