6.Find the present value.Amount Needed: $12,300Time (Years): 4Rate: 4%Compounded: quarterly$10,514.04$11,820.05$10,332.00$10,489.69

Accepted Solution

To solve this we are going to use the formula for  future value: [tex]FV=PV(1+ \frac{r}{n} )^{nt}[/tex]
[tex]FV[/tex] is the future value 
[tex]PV[/tex] is the present value 
[tex]r[/tex] is the interest rate in decimal form 
[tex]n[/tex] is the number of times the interest is compounded per year
[tex]t[/tex] is the time in years

We know for our problem that [tex]FV=12300[/tex], [tex]r= \frac{4}{100} =0.04[/tex], and [tex]t=4[/tex]. Since the interest is compounded quarterly, it is compounded 4 times per year; therefore, [tex]n=4[/tex]. Lets replace those values in our formula to find and solve for [tex]PV[/tex]:
[tex]FV=PV(1+ \frac{r}{n} )^{nt}[/tex]
[tex]12300=PV(1+ \frac{0.04}{4} )^{(4)(4)}[/tex]
[tex]PV= \frac{12300}{(1+ \frac{0.04}{4} )^{(4)(4)} }[/tex]

We can conclude that the present amount needed to have $12,300 after 4 years according to your given choices is $10,489.69