Math, asked by purnimakar, 11 months ago

how long will it take for a principal to double if money is worth 12% compounded monthly

Answers

Answered by Aman0990

Answer:

I believe you are asking if we have an annual rate of 12%, compounded monthly, how long to double?

1.01^X=2

X log(1.01) = log(2)

X = log(2)/log(1.01)

X = 69.66 or at 70 months.

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Answered by stalwartajk

Answer:

Precisely as time, it would take approximately 5.78 years for the principal to double at a rate of 12% compounded monthly

Step-by-step explanation:

The formula for calculating the future value of an investment with compound interest is:

FV = PV x (1 + r/n)^(n*t)
where:
FV = Future Value
PV = Present Value
r = Annual interest rate
n = Number of times compounded per year
t = Number of years
To answer this question, we need to find the value of t that would make the Future Value (FV) equal to 2 times the Present Value (PV), or FV = 2PV.
Let's plug in the given values:
r = 12% = 0.12
n = 12 (compounded monthly)
FV = 2PV
PV = 1 (we assume an initial investment of 1 dollar for simplicity)
So, the equation becomes:
2 = (1 + 0.12/12)^(12*t)
Taking the natural logarithm of both sides and solving for t, we get:
ln(2) = ln[(1 + 0.12/12)^(12t)]
ln(2) = 12t * ln(1 + 0.01)
t = ln(2)/(12*ln(1.01))
t ≈ 5.78

Therefore, it would take approximately 5.78 years for the principal to double at a rate of 12% compounded monthly.