SOLUTION: An investment earns 2.25% per annum, compounded daily. The number of years required for the investment to triple in value is...

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Question 1085860: An investment earns 2.25% per annum, compounded daily. The number of years required for the investment to triple in value is...
Found 2 solutions by jim_thompson5910, MathTherapy:
Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!
Use this compound interest formula
FV = PV*(1+r/n)^(n*t)
where,
FV = future value
PV = present value
r = interest rate in decimal form
n = number of times money is compounded per year
t = time in years

If we assume that $100 is invested, then we want to know the time t when the future value is $300. So PV = 100 and FV = 300 for some time t. The initial amount invested really doesn't matter because it will cancel out.

So we have
FV = 300
PV = 100
r = 0.025 (2.25% in decimal form)
n = 365 (assuming 365 days in a year)
t = unknown (we're solving for this)

Plug those values into the formula and solve for t

FV = PV*(1+r/n)^(n*t)
300 = 100*(1+0.0225/365)^(365*t)
300 = 100*(1+0.00006164383562)^(365*t)
300 = 100*(1.00006164383562)^(365*t)
300/100 = (1.00006164383562)^(365*t)
3 = (1.00006164383562)^(365*t)
Log[3] = Log[(1.00006164383562)^(365*t)]
Log[3] = (365*t)*Log[1.00006164383562]
Log[3]/Log[1.00006164383562] = 365*t
365*t = Log[3]/Log[1.00006164383562]
365*t = 17822.4819833315
365*t/365 = 17822.4819833315/365
t = 48.828717762552

So it will take roughly 48.828717762552 years for the investment to triple.

Answer by MathTherapy(10557) (Show Source):
You can put this solution on YOUR website!
An investment earns 2.25% per annum, compounded daily. The number of years required for the investment to triple in value is...

, where:
A = 3
P = 1
i = .0225
m = 365
We then get:
------- Converting to LOGARITHMIC form