SOLUTION: I can't do two questions. First is "Finance. Find the tripling time (To the next whole year) for money invested at 15% compounded annually." Second is "Finance. Find the doubling

Algebra ->  Customizable Word Problem Solvers  -> Finance -> SOLUTION: I can't do two questions. First is "Finance. Find the tripling time (To the next whole year) for money invested at 15% compounded annually." Second is "Finance. Find the doubling      Log On

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Question 238081: I can't do two questions.
First is "Finance. Find the tripling time (To the next whole year) for money invested at 15% compounded annually."
Second is "Finance. Find the doubling time (to two decimal places) for money invested at 10% compounded continuously."
I very need help with this problem.
Thank alot.
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
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.

continuous compounding formulas

discret compounding formulas