Question 997569: An investment of $10,000 with Barnes Bank earns a 2.42% APR compounded monthly.
Determine how long it will take the investment to double
Thank you in advance.
Answer by addingup(3677)   (Show Source):
You can put this solution on YOUR website! A= P(1+r/m)^mt, where
A is the future money, in your case 2 x 10,000= 20,000
P is the Principal, the amount we've invested = 10,000
r is the rate, the interest rate = 2.42%
n is the number of compounding periods in one year = 12
t is the number of years, this is what we'll find out.
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You double your money when A/P= 2, regardless of the amount of money. It's the interest rate and the time that dictate it. So here we go (NOTE: My calculator and I are not infallible. Do the math wherever you see calculations):
(1+r/m)^mt = 2
(1+.0242/12)^12t = 2
(1.00202)^12t = 2
Take the log of both sides
ln(1.00202)^12t = ln(2)
12t[ln(1.00202) = ln(2)
t= ln(2)/12*ln(1.00202)
t= 28.6 years
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