SOLUTION: Rose makes an investment worth Php 15,000 in a savings bank paying 14% compounded monthly. If she withdraws all her investments and the interest with amounts to Php 19, 450,how lon

Question 1178093: Rose makes an investment worth Php 15,000 in a savings bank paying 14% compounded monthly. If she withdraws all her investments and the interest with amounts to Php 19, 450,how long did she invest her money?
Answer by Theo(13342) (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.

in your problem:

f = 19450
p = 15000
r = 14% / 100 = .14 / 12 = .01166666667 per month.
n = the number of months you want to find.

the formula becomes 19450 = 15000 * (1 + .01166666667) ^ n

divide both sides of the equation by 15000 to get:
19450/15000 = (1 + .01166666667) ^ n
take the log of both sides of the equation to get:
log(19450/15000) = log((1 + .01166666667) ^ n)
since log(x^n) = n * log(x), this becomes:
log(19450/15000) = n * log(1.01166666667)
divide both sides of the equation by log(1.01166666667) to get:
log(19450/15000) / log(1.01166666667) = n
solve for n to get:
n = 22.39795036 months.

confirm this is correct by replacing n in the original equation with that to get:
f = 15000 * (1 + .01166666667) ^ 22.39795036 = 19450.

this confirms the solution is correct.

the solution is 22.39795036 months for 15000 to grow to 19450 at 14% interest per year compounded monthly.

you could also have used an online financial calculator to get the same results.

here are the inputs to that calculator.

here is the output from that calculator.

the calculator uses the percent rather than the rate.
the calculator rounds the answer to 2 decimal places.

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