is anyone any good at...?

Question

logarithms? I'm supposed to use logarithms to solve growth and decay problems. Can you explain how to do this problem?: Suppose $500 is invested at 6% annual interest compounded twice a year. When will the investment be worth $1000? Can anyone help me with this one? I think I can have this one explained I should be able to get the rest. thank you to anybody that can help.

Answer 1

Well, you have to use the formula

A = P ( 1 + r/n ) ^ (nt)

A = final amount of money
P = money you start out with
r = interest rate (must be in decimal form)
t = time in years
n = number of times compounded per year


So, first, you would plug in your numbers. You then get:

1000 = 500 ( 1 + .06/2 ) ^ 2t

Then divide each side by 500.

2 = ( 1 + .03 ) ^ 2t

Then you do the logs.

log (1+.03) 2 = 2t
(the (1+.03) is supposed to be below)

log 2 / log (1.03) = 2t

23.44977225 = 2t

Then divide both sides by 2.

11.72488613 = t