Question 1189643: How long will it take Php 2000 to earn Php 400 if the interest is 12% compounded semi annually
Answer by math_tutor2020(3817)   (Show Source):
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We start with Php 2000 and want to earn Php 400 in interest.
We want to find out how long it takes to reach a balance of Php 2400.
To find out, we use this compound interest formula
A = P*(1+r/n)^(n*t)
In this case,
A = 2400 = desired amount in t years
P = 2000 = principal or deposit amount
r = 0.12 = interest rate in decimal form
n = 2 = since we're compounding semi annually
t = unknown and what we want to solve for
So,
A = P*(1+r/n)^(n*t)
2400 = 2000*(1+0.12/2)^(2*t)
2400 = 2000*(1.06)^(2t)
2400/2000 = (1.06)^(2t)
1.2 = (1.06)^(2t)
Ln(1.2) = Ln( (1.06)^(2t) )
Ln(1.2) = 2t*Ln( 1.06 )
t = 0.5*Ln(1.2)/Ln(1.06)
t = 1.56448406760977 approximately
t = 2
It takes about 2 years for the money to go from Php 2000 to Php 2400.
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