Solve the problem.
-Suppose that you have $12,000 to invest. Which investment yields the greater return over 7 years: 8.75% compounded continuously or 8.9% compounded semiannually?
A)$12,000 invested at 8.9% compounded semiannually over 7 years yields the greater return.
B)$12,000 invested at 8.75% compounded continuously over 7 years yields the greater return.
C)Both investment plans yield the same return.

Question

Quizplus · Accepted Answer

The formula for continuously compounded interest is A = Pe^(rt), where A is the final amount, P is the principal, e is the base of the natural logarithm, r is the annual interest rate, and t is the time in years.The formula for semiannually compounded interest is A = P(1 + r/2)^(2t), where A is the final amount, P is the principal, r is the annual interest rate, and t is the time in years.Plugging in the values given in the problem, we get:For continuously compounded interest: A = 12000e^(0.0875*7) = 19,671.47For semiannually compounded interest: A = 12000(1 + 0.089/2)^(2*7) = 19,662.93Therefore, the investment that yields the greater return over 7 years is 8.75% compounded continuously.

Solve the Problem. -Suppose That You Have $12,000 to Invest. Which Investment Yields