9514 1404 393
Answer:
87 years
Step-by-step explanation:
The balance (A) in the continuously compounded account will be ...
A = P·e^(rt)
A = 6000·e^(0.06t)
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The balance (A) in the annually compounded account will be ...
A = P(1 +r)^t
A = 16000(1 +0.05)^t
These balances are equal when ...
6000·e^(0.06t) = 16000(1.05^t)
We can divide by 6000 to simplify this a little bit.
e^(0.06t) = 8/3(1.05^t)
Taking the natural logarithm gives ...
0.06t = ln(8/3) +t·ln(1.05)
t(0.06 -ln(1.05)) = ln(8/3) . . . . subtract t·ln(1.05) and factor)
t = ln(8/3)/(0.06 -ln(1.05)) ≈ 0.980829/0.0112098 ≈ 87.497
Rounded to the nearest year, the balances will be the same after 87 years.
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The balances will be about 1.14 million dollars.
