Solve the problem.
-Which has a lower present value: $30,000 if interest is paid at a rate of 5.98% compounded continuously for 5 years, or $33,000 if interest is paid at a rate of 3.3% compounded continuously for 65 months?
A)$33,000 with interest is paid at a rate of 3.3% compounded continuously for 65 months has a lower present value.
B)$30,000 with interest paid at a rate of 5.98% compounded continuously for 5 years has a lower present value.
C)Both investments have the same present value.

Question

Quizplus · Accepted Answer

To find the present value (PV) of each option, we use the formula for continuous compounding: $PV = Pe^{-rt}$, where $P$ is the future value, $r$ is the annual interest rate, and $t$ is the time in years. For the $30,000 at 5.98% for 5 years, $PV = 30000e^{-0.0598*5}$. For the $33,000 at 3.3% for 65 months (which is $65/12$ years), $PV = 33000e^{-0.033*(65/12)}$. Calculating these gives a lower present value for the $30,000 at 5.98% for 5 years, making option B correct.

Solve the Problem. -Which Has a Lower Present Value: $30,000 If Interest Is