SOLUTION: Suppose you deposit $1500 in a savings account that pays interest at an annual rate of 6%. No money is added or withdrawn from the account. How many years will it take for the acco

Question 1078090: Suppose you deposit $1500 in a savings account that pays interest at an annual rate of 6%. No money is added or withdrawn from the account. How many years will it take for the account to contain $2500?
Found 2 solutions by Boreal, addingup:
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
2500=1500(1+r)^n
5/3=(1+.06)^n
ln of both sides
0.5108=n ln (1+.06)
divide both sides by ln (1.06)
n=8.77 years.
Check
rule of 70 says that 70/interest rate is doubling time in years
this would predict doubling in 12 years; at almost 9, it has increased 2/3s This is reasonable.

Answer by addingup(3677) (Show Source): You can put this solution on YOUR website!
2500 = 1500(1+0.06)^t
So we have our unknown as a power function (^t). To solve, we need to use logs.
:
t = [log(A)-log(P)]/log(1+r) where A is the amount, P the principal, and r the rate.
t = [log(2500)-log(1500)]/log(1.06) = 8.88, or 8.9 years.
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Check:
2500 = 1500(1+0.06)^8.8 Correct, check it out, comes out to 2504 due to rounding.
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