SOLUTION: Compound Interest formula: A= P(1+(r/n))^nt I have to use this formula to answer this question: Determine how much time is required for an investment to double in value if int

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Compound Interest formula: A= P(1+(r/n))^nt I have to use this formula to answer this question: Determine how much time is required for an investment to double in value if int      Log On


   

Question 481218: Compound Interest formula:
A= P(1+(r/n))^nt
I have to use this formula to answer this question:
Determine how much time is required for an investment to double in value if interest is earned at a rate of 6.25% and compounded annually?
Please give me a detailed answer, I have tried using the formula myself but I keep getting stuck and am not having much success.
Thank you in advance for all your help! I really do appreciate it.
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
how much is required for an investment to double in value if the interest is earned at a rate of 6.25% and compounded annually?
formula to use is:
A = P(1+(r/n))^nt
A is the future amount
P is the present amount
r is the annual interest rate.
n is the number of compounding periods per year.
t is the number of years.
your annual interest rate is 6.25%.
you have to divide the percent interest rate by 100% to get the actual interest rate.
6.25% becomes .0625
this is your annual rate.
the 6.25% is your annual interest rate percent.
you set P equal to 1.
you set A equal to 2 (value of P when it is doubled).
n is equal to 1 because the number of compounding periods per year is set to 1.
r/n = .0625/1 = .0625
t*n = t
t is what you will be solving for.
your formula of:
A = P(1+(r/n))^nt becomes:
2 = 1 * (1.0625)^t which becomes:
2 = (1.0625)^t
take the log of both sides of this equation to get:
log(2) = log(1.0625^5) which becomes:
log(2) = t*log(1.0625)
this is because one of the properties of logarithmic equations is that log(a^b) = b*log(a).
divide both sides of this equation to get:
log(2)/log(1.0625) = t
use your calculator to solve for t to get:
t = 11.433426588
your money should double in 11.433426588 years.
plug that value into your original equation of:
2 = (1.0625)^t to get:
2 = (1.0625)^11.433426588
use your calculator to get:
2 = 2, confirming the value for t is good.
that's your answer.
your money will double in 11.433426588 years at an annual rate of .0625 compounded annually.