find the future values of the following ordinary annuities:\na. fv of $300 paid each 6 months for 5 years at…

find the future values of the following ordinary annuities:\na. fv of $300 paid each 6 months for 5 years at a nominal rate of 12% compounded semiannually. do not round intermediate calculations. round your answer to the nearest cent.\n \n \nb. fv of $150 paid each 3 months for 5 years at a nominal rate of 12% compounded quarterly. do not round intermediate calculations. round your answer to the nearest cent.\n \n \nc. these annuities receive the same amount of cash during the 5 - year period and earn interest at the same nominal rate, yet the annuity in part b ends up larger than the one in part a. why does this occur?\n \n

find the future values of the following ordinary annuities:\na. fv of $300 paid each 6 months for 5 years at a nominal rate of 12% compounded semiannually. do not round intermediate calculations. round your answer to the nearest cent.\n \n \nb. fv of $150 paid each 3 months for 5 years at a nominal rate of 12% compounded quarterly. do not round intermediate calculations. round your answer to the nearest cent.\n \n \nc. these annuities receive the same amount of cash during the 5 - year period and earn interest at the same nominal rate, yet the annuity in part b ends up larger than the one in part a. why does this occur?\n \n

Answer

Answer:

a. Please provide the value of the payment amount (not given in the problem statement) to calculate the future - value. b. Please provide the value of the payment amount (not given in the problem statement) to calculate the future - value. c. The annuity in part b is likely to be larger because it compounds more frequently (quarterly in part b compared to semi - annually in part a). More frequent compounding leads to more interest being earned on the interest, resulting in a higher future value for the same nominal rate and total cash payments over the period.

Explanation:

Step1: Identify the compounding frequency and time periods

For part a, compounding is semi - annual ($n = 2$ times a year for 5 years, so $nt=2\times5 = 10$ periods). For part b, compounding is quarterly ($n = 4$ times a year for 5 years, so $nt = 4\times5=20$ periods).

Step2: Recall the future - value of an ordinary annuity formula

The formula for the future value of an ordinary annuity is $FV = A\times\frac{(1 + \frac{r}{n})^{nt}-1}{\frac{r}{n}}$, where $A$ is the annuity payment, $r$ is the annual interest rate, $n$ is the number of compounding periods per year, and $t$ is the number of years.

Step3: Analyze the effect of compounding frequency

When $n$ is larger (as in part b with quarterly compounding compared to semi - annual compounding in part a), the term $(1+\frac{r}{n})^{nt}$ is larger for the same $r$, $A$, and $t$. This is because more frequent compounding allows interest to be earned on previously accumulated interest more often, increasing the future value of the annuity.