SOLUTION: Mariel deposits Php 50,000 in a savings account. The account pays 6% annual interest. How many years will it take for her money to grow up to Php 89,542

Question 1189632: Mariel deposits Php 50,000 in a savings account. The account pays 6% annual interest. How many years will it take for her money to grow up to Php 89,542
Found 2 solutions by math_tutor2020, Theo:
Answer by math_tutor2020(3816) (Show Source): You can put this solution on YOUR website!

We use this compound interest formula
A = P*(1+r/n)^(n*t)

In this case,
A = 89,542 = desired amount in t years
P = 50,000 = principal or deposit amount
r = 0.06 = interest rate in decimal form
n = 1 = since we're compounding annually
t = unknown and what we want to solve for

So,
A = P*(1+r/n)^(n*t)
89542 = 50000*(1+0.06/1)^(1*t)
89542/50000 = (1.06)^t
1.79084 = (1.05)^t
Ln(1.79084) = Ln( (1.06)^t )
Ln(1.79084) = t*Ln( 1.06 )
t = Ln(1.79084)/Ln(1.06)
t = 9.9999262433654 approximately

It takes about 10 years for the money to reach the desired goal of Php 89,542.

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
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.

when the time periods are in years and the interest rate is 6% per year and the present value is 50,000 and the future value is 89,542, the formula becomes:

89,542 = 50,000 * (1 + .06) ^ n
divide both sides of the equation by 50,000 and simplify the right side of the equation to get:
89,542/50,000 = 1.06 ^ n
take the log of both sides of the equation to get:
log(89,542/50,000) = log(1.06^n) which becomes:
log(89,542/50,000) = n*log(1.06)
divide both sides of the equation by log(1.06) to get
log(89,542/50,000)/log(1.06) = n
solve for n to get:
n = 9.999926243.
replace n in the original equation with that and solve for f to get:
f = 50,000 * 1.06^9.999926243 = 89,542.
this confirms the value of n is good.
your solution is that it will take 9.999926243 years for her money to grow to 89,542.

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