find the present value and the amount of interest earned. use the present value of a dollar table. amount…

Explanation:

Step1: Identify compound - ing periods and rate per period

The time $t = 9$ years. Since it is compounded quarterly ($n = 4$ times a year), the number of compounding periods $m=nt=9\times4 = 36$. The annual interest rate $r = 6%=0.06$, so the interest rate per period $i=\frac{r}{n}=\frac{0.06}{4}=0.015$. The future value $A = 18698$.

Step2: Use the present - value formula

The present - value formula for compound interest is $P=A(1 + i)^{-m}$. Substitute $A = 18698$, $i = 0.015$, and $m = 36$ into the formula: $P=18698\times(1 + 0.015)^{-36}$. First, calculate $(1 + 0.015)^{-36}=\frac{1}{(1.015)^{36}}$. Using a calculator, $(1.015)^{36}\approx1.709137$. Then $\frac{1}{(1.015)^{36}}\approx0.58509$. So, $P=18698\times0.58509\approx10941.91$.

Step3: Calculate the interest earned

The interest earned $I=A - P$. Substitute $A = 18698$ and $P\approx10941.91$ into the formula. $I=18698-10941.91 = 7756.09$.

Answer:

The present value is $$10941.91$. The interest earned is $$7756.09$.