How do I answer compounding money question using ln?

Question

The question is the following:
How many years would it take an amount of money to triple if it is invested at 5% compounded continuously?

The choices for answers are the following:
ln3
5ln3
10ln3
20ln3
25ln3
2ln3

I don't need the answer necessarily, but how to solve these types of problems?

Answer 1

3 = exp^(.05y). This is the formula derived from taking the limit of (1+r/n)^yn where n --> infinity. This represents future value of a unit, and in general p(1+r/n)^yn, n--> infinity is compounding p continuously at rate r for y years.

Here we know that 3 is the result, and so
ln(3) = .05y, or y = 20ln(3)

Answer 2

More than 23 years, and less than 24.-
It can be established with accurate precision as I'll explain later.
I'm not an accountant, who have formulas and "financial" calculators to find the answer.
I use "Microsoft Excel"
In the first column, I put the number of years. 1,2,3,4 ....
In the second one, my amount of money, year after year.
In the third column, I put the interests I win every year.
The second column is made as the addition of the amount pf money I had the previous year year, plus the interests earned in the previous year.
Use the function copy, and g downwards.
You'll get the answer I gave you.
If you want to know the amount of months over 23 years, instead of using the rate 5%, you use the monthly rate, wich will be (1.05)^(1/12) - 1 = 0.00474 %
If you want to now the number of days, you use the daily rate, which will be (1.05)^(1/360) - 1 = 0.0001355%

Answer 3

Hi,
Let's start with the equation for continuously compounding interest:
A = Pe^(rt) where A is the amount, P is the prinicpal (the original investment), r is the rate as a decimal, and t is the time in years.
A/P =e^(rt) (Divide by P)
ln A/P = rt (Take the ln of both sides.)
t = (ln A/P)/r
t = (ln 3)/.05 A/P = e and the interest is .05
t = 20 ln 3 (On the right side multiple both numerator and denominator by 20.

Hope this helps.
FK

Answer 4

set up an equation, in this case (i'm not 100% sure its exactly right, but you can tweak it):

(1.05^n)x=3x

n being the number of years, x being the money.

My thinking on this is that multiplying by 1.05 is the same as adding 5%, and this is done repeatedly because it is compounded. you're trying to find the number of times this is done, n, so that it equals 3 times the original number, x.

Answer 5

i think of the main suitable formula is A=P(a million+r)^n, the place n is the era in many cases in years. In 40years, it extremely is going to quantity to: A=800(a million+0.a million)^40 =US$36,207.40 the money will triple in n years: 2400=(a million+r)^n =(a million+0.a million)^n 2400=(a million.a million)^n nth root of 2400=a million.a million