Use the compound interest formulas A $$A = P \left( 1 + \frac { r } { n } \right) ^ { n t }$$ and A = Pert to solve.
-Suppose that you have $9000 to invest. Which investment yields the greater return over 7 years: 7.5% compounded continuously or 7.6% compounded semiannually?
A) $9000 invested at 7.5% compounded continuously over 7 years yields the greater return.
B) Both investment plans yield the same return.
C) $9000 invested at 7.6% compounded semiannually over 7 years yields the greater return.

Question

Quizplus · Accepted Answer

The formula for continuously compounded interest is A = Pert, where P is the principal, r is the annual interest rate, and t is the time in years. The formula for semiannually compounded interest is A = P(1 + r/n)^(nt), where P is the principal, r is the annual interest rate, n is the number of times per year that the interest is compounded, and t is the time in years.In this case, we have P = $9000, r = 7.5%, and t = 7 years. If we use the formula for continuously compounded interest, we get:A = Pert = $9000e^(0.075*7) = $12,214.03If we use the formula for semiannually compounded interest, we get:A = P(1 + r/n)^(nt) = $9000(1 + 0.076/2)^(2*7) = $12,198.76Therefore, the investment that yields the greater return over 7 years is 7.5% compounded continuously.

Use the Compound Interest Formulas A A=P(1+rn)ntA = P \left( 1 + \frac { r } { n } \right) ^ { n t }A=P(1+nr​)nt

Use the Compound Interest Formulas A $A = P \left( 1 + \frac { r } { n } \right) ^ { n t }$