In how many years will money triple at 6.4% compounded monthly?
A) 206.53 years
B) 17.71 years
C) 17.21 years
D) 1.48 years
E) 2.57 years

Question

Quizplus · Accepted Answer

We can use the formula for compound interest with monthly compounding:
A = P*(1+r/12)^(12*t)
where A is the amount, P is the principal (starting amount), r is the annual interest rate (as a decimal), and t is the time (in years).

We want to know when the amount will triple, so we can set up the equation:
3P = P*(1+0.064/12)^(12*t)
Divide both sides by P:
3 = (1+0.064/12)^(12*t)
Take the natural logarithm of both sides:
ln(3) = 12*t*ln(1+0.064/12)
Divide both sides by 12*ln(1+0.064/12):
t = ln(3)/(12*ln(1+0.064/12)) ≈ 17.21 years

Therefore, the best choice is C.

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