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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Solution :-
Let the principal (P) be 'x' then the Amount (A) will be 4x.
As the interest is compounded monthly
Rate of interest = 10.1 % = 10.1/(100*12) = 0.101/12
Time (t) = 12t
∴ A = P[1 + R/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 (Approx)
So, approximately in 13 years 9 months she will have 4 times the amount of money that she actually has right now.
Answer
Let the principal (P) be 'x' then the Amount (A) will be 4x.
As the interest is compounded monthly
Rate of interest = 10.1 % = 10.1/(100*12) = 0.101/12
Time (t) = 12t
∴ A = P[1 + R/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 (Approx)
So, approximately in 13 years 9 months she will have 4 times the amount of money that she actually has right now.
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