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3 years ago

5

Stuart put $99 into a CD that pays 2.6% interest, compounded monthly. According to the Rule of 72, approximately how long will i

t take for his money to double? Round to the nearest tenth. Show your work.

2 answers:

Temka [501]3 years ago

6 0

Answer: 27 years (approx)

Step-by-step explanation:

According to the Rule of 72,

If the product of interest rate and time is equal to 72, the amount will be doubled.

According to the question,

The annual rate = 2.6%

Let after t years the amount will be doubled.

Thus, 2.6 × t = 72

$t = \frac{72}{2.6} = 27.6923076923$

Since, the actual time will always less than the time gets by the 72 rule.

Thus, Approx 27 year after the amount will be doubled.

Taya2010 [7]3 years ago

4 0

72/2.6=27.7 years
Hope it helps :-)

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$e^{\ln |P|} = e^{-k_1t + c_1} \quad e^{\ln |Q|} = e^{-k_12t + c_2}$

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$P = C_1e^{-k_1t} \quad Q = C_2e^{-k_2t}$ ,

where $C_1 := \pm e^{c_1}$ and $C_2 := \pm e^{c_2}$ .

Since the amounts of the uranium isotopes were the same initially, we obtain the initial condition

$P(0) = Q(0) = C$

Substituting 0 for $P$ in the general solution gives

$C = P(0) = C_1 e^0 \implies C= C_1$

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$P = Ce^{-k_1t} \quad Q = Ce^{-k_2t}$

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$\tau = \frac{\ln 2}{k}$

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We have that

$\frac{P(t)}{Q(t)} = 137.7$

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