Question 1189628: If a Php 25,000 investment receives 5% interest each year, after how many years will the investment have doubled in value
Answer by math_tutor2020(3817)   (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 = 50,000 = because we wish to double the deposit amount P
P = 25,000 = principal or deposit amount
r = 0.05 = interest rate in decimal form
n = 1 = since we're compounding annually
t = unknown
So,
A = P*(1+r/n)^(n*t)
50000 = 25000*(1+0.05/1)^(1*t)
50000/25000 = (1.05)^t
2 = (1.05)^t
Ln(2) = Ln( (1.05)^t )
Ln(2) = t*Ln( 1.05 )
t = Ln(2)/Ln(1.05)
t = 14.206699 approximately
t = 15 years
It takes approximately 15 years for the money to double.
Note the rule of 72 says
72/5 = 14.4
which is fairly close to the 14.206699 value we got earlier.
To use this rule, we simply divide the value 72 over the numeric form of the interest rate. We treat the "5" as is without the percent sign.
For more info, check out this page
https://www.basic-mathematics.com/why-the-rule-of-72-works.html
Other things to notice
A(t) = 25000(1.05)^t
A(14) = 49,498.29
A(15) = 51,973.20
which helps confirm that 14 years is just a bit shy of the goal of Php 50,000; while 15 years will get you over the hurdle.
Once again, the final answer is approximately 15 years
|
|
|
