Solve the problem.
-If Emery has $1200 to invest at 8% per year compounded monthly, how long will it be before he has $2400? If the compounding is continuous, how long will it be? (Round your answers to three decimal
Places.)
A)8.693 yrs, 8.664 yrs
B)0.751 yrs, 0.722 yrs
C)80.889 yrs, 8.914 yrs
D)0.113 yrs, 0.866 yrs

Question

Quizplus · Accepted Answer

Using the formula for compound interest, we have:
$2400 = 1200(1 + \frac{0.08}{12})^{12n}$ where n is the number of years.
Solving for n using logarithms, we get $n = \frac{ln 2}{12 ln (1 + \frac{0.08}{12})} \approx 8.693$ years.
For continuous compounding, we use the formula A = Pe^{rt}, where A is the final amount, P is the principal, r is the interest rate, and t is the time in years.
We want to solve for t when P = 1200, A = 2400, and r = 0.08.
Substituting the values, we have $2400 = 1200e^{0.08t}$.
Solving for t using logarithms, we get $t = \frac{ln 2}{0.08} \approx 8.664$ years.

Solve the Problem. -If Emery Has $1200 to Invest at 8% Per Year