Question 776078: Determine how much time is required for an investment to triple in value if interest is earned at the rate of 5.75% compounded annually Found 2 solutions by DrBeeee, MathTherapy:Answer by DrBeeee(684) (Show Source):
You can put this solution on YOUR website! The formula is
(1) B = P*(1+r)^n
What we need here is to determine n to make factor,
(2) (1+r)^n = 3 when r = 5.75% or
(3) (1+0.0575)^n = 3 or
(4) (1.0575)^n = 3
To solve for we need to use logarithms. Take the natural (or LOG) of each side to get
(5) ln((1.0575)^n) = ln(3) or
(6) n*ln(1.0575) = ln(3) or
(7) n = ln(3)/ln(1.0575)
Use your scientific calculator to get
(8) n = 1.0986../0.055907.. or
(9) n = 19.65..
Let's check this using (4).
Is ((1.0575)^19.65 = 3)?
Is (2.9999... = 3)? Yes
Answer: The investment will triple in about 19y 7m 24d 4h, when the compounded interest rate is 5.75%.
You can put this solution on YOUR website!
Determine how much time is required for an investment to triple in value if interest is earned at the rate of 5.75% compounded annually
Tripling in value makes the future value (A), 3P
Therefore, becomes:
t = ----- Applying change of base
t, or time = years
You can do the check!!
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