a. use the appropriate formula to find the value of the annuity.\nb. find the interest.\nperiodic deposit |…

a. use the appropriate formula to find the value of the annuity.\nb. find the interest.\nperiodic deposit | rate | time\n$1500 at the end of every three months | 6.25% compounded quarterly | 6 years\nclick the icon to view some finance formulas.\na. the value of the annuity is $ .\n(do not round until the final answer. then round to the nearest dollar as needed.)

a. use the appropriate formula to find the value of the annuity.\nb. find the interest.\nperiodic deposit | rate | time\n$1500 at the end of every three months | 6.25% compounded quarterly | 6 years\nclick the icon to view some finance formulas.\na. the value of the annuity is $ .\n(do not round until the final answer. then round to the nearest dollar as needed.)

Answer

Explanation:

Step1: Identify the variables

$P = 1500$, $r=0.0625$, $n = 4$ (quarter - ly compounding), $t = 6$

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

The formula for the future - value of an ordinary annuity is $A=P\times\frac{(1 + \frac{r}{n})^{nt}-1}{\frac{r}{n}}$. Substitute the values: $\frac{r}{n}=\frac{0.0625}{4}=0.015625$, $nt=4\times6 = 24$. $A = 1500\times\frac{(1 + 0.015625)^{24}-1}{0.015625}$

Step3: Calculate $(1 + 0.015625)^{24}$

$(1 + 0.015625)^{24}\approx1.442973$

Step4: Calculate the numerator

$(1 + 0.015625)^{24}-1\approx1.442973 - 1=0.442973$

Step5: Calculate the value of the annuity

$A = 1500\times\frac{0.442973}{0.015625}=1500\times28.350272\approx42525$

Step6: Calculate the total amount of deposits

The total amount of deposits is $1500\times4\times6=36000$

Step7: Calculate the interest

Interest $=A -$ total deposits. Interest $=42525-36000 = 6525$

Answer:

a. $42525$ b. $6525$