Question 238081
money invested at 15% a year compounded annually is solved using the following formula.


FV = PA * (1+i/c)^(n*c) 


where:


FV = future value
PA = present amount
i = annual interest rate
c = number of compounding periods per year
n = number of years.


in your problem:


FV is equal to 3.
PA is equal to 1.
i = 15% per year / 100% = .15
c = 1
n = what you want to find.


your equation becomes:


3 = 1 * (1.15)^n


this becomes:


3 = 1.15^n


take the log of both sides of this equation to get:


log(3) = log(1.15^n)


since log(x^a) = a*log(x), this means that your equation becomes:


log(3) = n*log(1.15)


divide both sides of this equation by 1.15 to get:


n = log(3)/log(1.15) = 7.860596884


the money will triple in 7.860596884 years.


put this value into your original equation to get:


3 = 1.15^7.860596884 = 3


answer is confirmed.


it would take 8 years if your round up to the next whole years.


your second problem is done as follows:


find the doubling time.


continuous compounding is a different formula.


that formula is:


FV = PA * e^(r*n)


where:


FV = future value
PA = present amount
e = scientific constant of 2.718281828...
r = annual interest rate
n = number of years.


in your equation:


FV = 2
PA = 1
e = 2.718281828 (always)
r = 10% / 100% = .1
n = what you want to find.


your equation becomes.


2 = 1 * e^(.1*n)


this equation becomes:


2 = e^(.1*n)


take the log of both sides of this equation to get:


log(2) = log(e^(.1*n))


since log (x^a) = a*log(x), your equation becomes:


log(2) = .1*n*log(e)


divide both sides by log(e) * .1  to get:


log(2)/log(e) / .1 = n which is the same as:


n = log(2)/log(e) / .1


solve for n to get:


n = 6.931471806


your money will double in 6.931471806 years


plug this into your original equation to get:


2 = e^(6.931471806*.10) = 2


round up to the nearest year and you get 7 years to double your money using continuous compounding.


check these lessons out to see what this is all about.


<a href = "http://www.algebra.com/algebra/homework/Finance/theo-20090921.lesson" target = "_blank">continuous compounding formulas</a>


<a href = "http://www.algebra.com/algebra/homework/Finance/FINANCIAL-FORMULAS-101.lesson" target = "_blank">discret compounding formulas</a>