Financial Models

Question

9)  How long does it take for an investment to double in value if it is invested at 2% compounded monthly? Compounded continuously?

Answer 1

I go through in detail how to do each part of the problem.

Answer 2

2 = 1*[1+ (0.02/12)]^12t

2 /1= 2 = [1+ (0.02/12)]^12t

For simplicity, let R = 1+ (0.02/12)

2 = R^12t

log _R (2) = log _R R^2t = 2t

2t = log _R (2)

t = [log _R (2)] / 2 = [ log (2) / log (R) ] / 2

t = 34.686 years

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2 = 1 * e^0.02t

200/100 = 2 = e^0.02t

ln(2) = 0.02t

t = ln(2) / 0.02

t = 34.657 years

Answer 3

aren't the equatiions

1.for monthly,,P(t)=P(1+(.02/12))^t,,,,,where t is in months. If P(t)=2P

then t=ln(2)/(1+(.02/12)) or 416 months=34.67 years

2.for continuous,,,P(t)=P*e^.02t,,,,,where t is in years. If P(t)=2P

then t=ln(2)/.02 or t=34.66 years