SOLUTION: The rule of 72 is a rule of thumb for finding how long it takes money at interest to double:� If r is the annual interest rate, then the doubling time is approximately 72/(1
Algebra.Com
Question 1035061: The rule of 72 is a rule of thumb for finding how long it takes money at interest to double:� If r is the annual interest rate, then the doubling time is approximately 72/(100r) years.
(a) Calculate the balance at the end of the predicted doubling time for each $1000, with annual compounding, for the small growth rates of 3%, 4%, and 6%
b) Repeat part (a) for the intermediate interest rates of 8% and 9%.
(c) Repeat part (a) for the larger interest rates of 12%, 24%, and 36%.
(d)What do you conclude about the rule of 72?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
f = p * (1+r)^n
f = future value
p = present value
r = interest rate per time period
n = number of time periods.
when you compound annually, r is the annual interest rate and n is the number of years.
if you divide both sides of the equation by p, you get:
f/p = (1+r)^n
if your present value doubles, then f/p = 2
you wind up with 2 = (1+r)^n
take the natural log of both sides of this equation to get:
ln(2) = ln(1+r)^n
since log(a^b) = b*log(a), your equation becomes:
ln(2) = n*ln(1+r).
solve for n to get n = ln(2) / ln(1+r).
when r = .03, this becomes n = ln(2) / ln(1.03)
when r = .04, this becomes n = ln(2) / ln(1.04)
when r = .06, this becomes n = ln(2) / ln(1.06)
solve for n and you get:
when r = .03, n = 23.45
when r = .04, n = 17.67
when r = .06, n = 11.90
using the rule of thumb, .....
when r = .03, n = 72/3 = 24
when r = .04, n = 72/4 = 18
when r = .06, n = 72/6 = 12
that's a pretty close estimate to the actual calculations.
rule of 72 looks like it works pretty good.
RELATED QUESTIONS
A rule of thumb for finding how long it takes an investment to double is called the rule... (answered by checkley77)
The amount of money in an account with continuously compounded interest is given by the... (answered by robertb)
The amount of money in an account with continuously compounded interest is given by the... (answered by ikleyn,MathTherapy)
Please Help I dont understand the 72 Rule.
Use the rule of 72 to estimate how long it... (answered by MathLover1)
The amount of money in an account with continuously compounded interest is given by the... (answered by drk,stanbon)
The amount of money in an account with continuously compounded interest is given by the... (answered by nerdybill)
The amount of money in ana ccount with continuoudly compounded interest is given by the... (answered by stanbon)
The amount of money in an account with continuously compounded interest is given by the... (answered by richwmiller)
The rule of 72 states that if an investment earns p % interest per year, it will take... (answered by Theo)