# Integrated Trig

How many years will it take for an initial investment of \$5,000 to double if it is invested at a rate of 3% compunded continuously? Compounded annually?

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1. 5000 e^(.03t) = 10000
e^(.03t) = 2
take ln of both sides , and use rules of logs
.03t = ln 2
t = ln 2/.03 = appr 23.1 years

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2. if compounded annually

1.03^t = 2
t ln1.03 = ln2
t = ln2/ln1.03 = appr 23.45 years

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