SOLUTION: Xian opened a savings account and put Php 6,250 in it. Each year, the account increases by 20%. How many years will it take the account to reach Php 12,960?
Question 1170595: Xian opened a savings account and put Php 6,250 in it. Each year, the account increases by 20%. How many years will it take the account to reach Php 12,960? Found 2 solutions by Theo, MathTherapy:Answer by Theo(13342) (Show Source): You can put this solution on YOUR website! the formula to use if f = p * (1 + r) ^ n
f = future value
p = present value
r = interest rate per time period.
n = number of time periods.
in your problem, the formula becomes 12,960 = 6,250 * (1 + .2) ^ n
the interest rate in the formula is equal to the interest rate percent divided by 100.
that's why the interest rate per time period is equal to 20% / 100 = .2
you want to solve for n.
divide both sides of the equation by 6,250 to get:
12,960 / 6,250 = (1 + .2) ^ n
take the log of both sides of the equation to get:
log(12,960 / 6,250) = log((1 + .2) ^ n)
since log((1 + .2) ^ n) = n * log(1 + .2), the equation becomes:
log(12,960 / 6,250) = n * log(1 + .2)
divide both sides of the equation by log(1 + .2) to get:
log(12,960 / 6,250) / log(1 + .2) = n
solve for n to get:
n = 4.
that's your solution.
confirm the solution is good by replacing n in the original equation to get:
12,960 = 6,250 * (1 + .2) ^ 4
solve to get:
12,960 = 12960.
Let the time it takes for the account to have PhP 12,960, be t
Then we get:
Converting to LOGARITHMIC form, the time it takes for the account to have PhP 12,960, or