Question

Determine the time necessary for P dollars to double when it is invested at interest rate r compounded annually, monthly, daily, and continuously. (Round your answers to two decimal places) r=8%​

Answer 1

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Answer:

• annually: 9.01 years
• monthly: 8.69 years
• daily: 8.67 years
• continuously: 8.66 years

Explanation:

For interest compounded in discrete intervals, the formula is ...

A = P(1 +r/n)^(nt)

We want to find t for P=1 and A=2, so we have ...

2 = (1 +r/n)^(nt)

ln(2) = nt·ln(1+r/n)

t = ln(2)/(n·ln(1+r/n))

A table of values for r=0.08 is attached.

__

For continuous compounding, the formula is ...

A = Pe^(rt)

t = ln(A/P)/r = ln(2)/0.08 ≈ 8.66434 . . . . years

__

• annually: 9.01 years
• monthly: 8.69 years
• daily: 8.67 years
• continuously: 8.66 years