SOLUTION: Please help me solve this word problem: in 1991, the average cost of attending a public university through graduation. Was $20,972. If johns parents deposited that amount in an

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Question 1104551: Please help me solve this word problem:
in 1991, the average cost of attending a public university through graduation. Was $20,972. If johns parents deposited that amount in an account in 1991 at an interest rate of 7% compounded semi-annually, how long will it take for the money to double? Round answer to two decimals.
Found 2 solutions by Boreal, Theo:
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
P=Po(1+r/2)^2t, t is years
Any amount to double is where P=2Po
so 2=(1+0.035)^2t
ln2=2t ln(1.035)
2t=ln 2/ln (1.035)
t=10.07 years
as a rough check, the rule of 72 would predict 10.29 years.

Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
the formula to use 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 time periods are in semi-annual periods which means 2 time periods per year.

your present value is 20792.
your future value is 2 * 20792.
your interest rate per time period is .07 per year / 2 time periods per year = .035.
your number of time periods is n.

the formula becomes 2 * 20792 = 20792 * (1.035) ^ n.

divide both sides of this equation by 20792 to get 2 = 1.035 ^ n.

take the log of both sides of this equation to get log(2) = log(1.035 ^ n).

since log(1.035 ^ n) is equal to n * log(1.035), this equation becomes log(2) = n * log(1.035).

divide both sides of this equation by log(1.035) to get log(2) / log(1.035) = n.

solve for n to get n = log(2) / log(1.035) = 20.14879168 time periods.

since there are 2 time periods per year, then it will take 20.14879168 / 2 = 10.07439584 years.

round this to 2 decimal places, and it will take 10.07 years.