Mdrs D.
asked • 05/31/17Math quick
How long will it take money to triple if it is invested at the following rates?
(A) 5.7% compounded monthly
(B) 12% compounded monthly
(A) 5.7% compounded monthly
(B) 12% compounded monthly
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2 Answers By Expert Tutors
Xavier H. answered • 05/31/17
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Excellent Math and Science Tutor
Start with the general equation for P = Po(1 + i)
Xavier H.
The answer section didn't provide my entire reply. So, in short start with general equation
P = Po (1+i/a)at , where P is the future principal, Po is the initial principal, i is the annual interest rate, t is the period in years, and a is the compounding factor (in our case a is 12 because of monthly compounding).
Now solve for t
(P/Po) = (1+i/a)at
ln(P/Po) = (at)*ln(1+i/a) -----> you can use log() instead of ln()
t = ln(P/Po) / (a ln(1+i/a))
Now plug in your values to get your answer for t.
(A) 5.7% Compounded monthly
t = ln(3)/(12*ln(1+0.057/12))
t = 19.3196
t = 19.32 years
Report
05/31/17
Ok. For compound interest problems, we can use the formula: A = P(1 + i)n
A = the accumulated amount, P = the principal (amount invested), i = the interest rate, n = the amount of time
We want to know when A = 3P
At 5.7%, we have:
3P = P(1 + 0.057/12)12n
3 = (1 + 0.057/12)12n
3 = (1.0475)12n
ln 3 = ln(1.0475)12n
ln 3 = 12n(ln(1.0475))
n = 1.97 years
Use the same procedure for the interest rate of 12% compounded monthly
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Michael A.
05/31/17