Financial Models

Question

8)  If Tanisha has $100 to invest at 7% per annum compounded semiannually, how long will it be before she has $200? If the compounding is continuous, how long will it be?

Answer 1

200 = 100*[1+ (0.07/2)]^2t

200/100 = 2 = [1+ (0.07/2)]^2t = [1 +0.035]^2t

log _1.035 (2) = log _1.035 [1 +0.035]^2t = 2t

2t = log _1.035 (2)

t = [log _1.035 (2)] / 2 = { [log (2)] / [log(1.035)] } / 2

t = 10.074 years

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200 = 100 * e^0.07t

200/100 = 2 = e^0.07t

ln(2) = 0.07t

t = ln(2) / 0.07

t = 9.902 years