A high-yield savings pays 20% interest, compounded continuously. How long would it take an initial investment of $2500 to grow to $20,000?
A) 1.04 years
B) 103.972 years
C) 10.397 years
D) 14.979 years
E) none of these

Question

Quizplus · Accepted Answer

We can use the formula for continuous compounding:
A = Pe^(rt)
Where A is the final amount, P is the initial investment, e is the Euler's number (approximately 2.71828), r is the interest rate, and t is the time in years.
Plugging in the given values, we get:
$20,000 = $2500e^(0.2t)
Dividing both sides by $2500 and taking the natural logarithm of both sides, we get:
ln(8) = 0.2t
t = ln(8)/0.2
t ≈ 10.397 years
Therefore, the correct answer is C: 10.397 years.

A High-Yield Savings Pays 20% Interest, Compounded Continuously