How long does it take for an investment to double in value i

How long does it take for an investment to double in value if it is invested at 2% compounded quarterly? Compounded continuously? At 2% compounded quarterly, the investment doubles in about years. (Round to two decimal places as needed.) At 2% compounded continuously, the investment doubles in about years. (Round to two decimal places as needed.)

Solution

Solution : Rate =2% quarterly, time =?

For compounded quarterly:

We know that amount after t years.

2P=P(1+.2/4)^4t

2=(1.05)^4t

Taking log of both sides

log 2 = 4t log(1.05)

t = log 2/(4*log(1.05))

Thus t = 3.55 years. Ans.

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For compounded continuous:

2P = Pe^(0.2t)

or 2 = e^0.2t

Taking natural log of both sides

ln2 = 0.2t

or t = ln2 /0.2

Thus t = 3.46 years. Ans.