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Buffy just put some money into a CD that pays 10.1% interest, compounded monthly. According to the rule of 72, in approximately how many years will she have 4 times the amount of money that she has now?
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Jun 19, 2019
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Buffy just put some money into a CD that pays 10.1% interest, compounded monthly. According to the rule of 72, in approximately how many years will she have 4 times the amount of money that she has now?
Mathematics
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JennEDVT
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Answer:
14.3 years is correct
Explanation:
Berndinox
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Jun 21, 2019
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Let the principal be 'x' then the Amount will be 4x.
As the interest is compounded monthly:
Rate of interest = 10.1 % = 10.1/(100*12) = 0.101/12
Time = 12t
Amount = Principal[1 + Rate/100]
⇒ 4x = x[1 + 0.101/12]¹²t
⇒ 4x/x [1 + 0.008416667]¹²t
⇒ 4 = [1.008416667]¹²t
⇒ log(4) = log[1.008416667]¹²t
⇒ 0.602059991327 = [0.003640014891]¹²t
⇒ 12t = 0.602059991327/0.003640014891
⇒ 12t = 165.400419876
⇒ t = 165.400419876/12
t = 13.78 years or 13 years 9 months.
So, it is about 13 years 9 months she will have 4 times the amount of money.
Vano
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Jun 23, 2019
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