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Question 1003761: In how many years time will a sum of money quintuple at a rate of 4% per annum compounded quarterly?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the general formula is:
f = p * (1+r)^n
f is the future value
p is the present value
r is the interest rate per time period.
n is the number of time periods.
your problem wants to know when your money will quintuple if you invest it at 4% per year compounded quarterly.
your compounding periods per year are 4.
your number of time periods will be 4 * the number of years.
your interest rate per time period will be the annual interest rate divided by 4.
4% per year give you an interest rate of .04 per year.
divide that by 4 and you get an interest rate of .01 per time period, with each time period being a quarter of a year.
you want to quintuple our money, so set f = 5 and p = 1.
the formula of f = p * (1+r)^n becomes:
5 = 1 * 1.01^n
this can be written as 5 = 1.01^n because 1 times anything is equal to anything.
so you start with 5 = 1.01^n
take the log of both sides of this equation to get log(5) = log(1.01^n).
since log(1.01^n) is equivalent to n * log(1.01), your equation becomes:
log(5) = n * log(1.01)
divide both sides of this equation by log(1.01) to get:
log(5) / log(1.01) = n
use your calculator to solve for n to get:
n = 161.7471757
since your time period is in quarters of a year, you need to divide that by 4 to get the number of years.
your solution is that the number of years for your money to quintuple is 40.43679392 years.
to prove this is correct, go back to your formula and replace n with 4 * 40.43679392 to get 161.7471757 and your equation will become:
5 = 1 * 1.01^161.7471757
solve this equation to get 5 = 5
this confirms the equation is correct.
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