Question

victor puts aside $12000 in an account with interest compounded continuously at 2.3%. how long will it take for him to earn 3000? round to the nearest month.

Answer 1

Victor will need approximately 138 months, or 11.53 years, to earn $3000 with continuously compounded interest at a rate of 2.3%.

Step-by-step explanation:

To calculate the time it will take for Victor to earn $3000 with continuously compounded interest, we can use the formula A = P * e^(rt), where A is the final amount, P is the initial amount, e is Euler's number (approximately 2.71828), r is the interest rate, and t is the time.

In this case, P = $12000, A = $15000, and r = 2.3%. We can substitute these values into the formula and solve for t:

$15000 = $12000 * e^(0.023t)

Divide both sides by $12000:

e^(0.023t) = 1.25

Take the natural logarithm of both sides:

ln(e^(0.023t)) = ln(1.25)

0.023t = ln(1.25)

Divide both sides by 0.023:

t = ln(1.25) / 0.023

Using a calculator, we find that t is approximately 11.53 years.

However, the question asks for the time rounded to the nearest month. Since there are 12 months in a year, we can multiply 11.53 by 12 to convert it to months and round to the nearest whole number:

t = 11.53 * 12 = 138.36, rounded to 138 months.