we have
A= P 950
n= 6years and 6 months quaterly then
6 years + 6months = 78 months
78 moths quarterly = 19.4 quarters
then n=19
Since we are talking about compounded quarterly, this means the money change every 4 months by a rate of 5%
this means in months 1,2 and 3 the rate is not affecting the amount is not until month 4 the rate affect the amount
then when we said n=19 we are saying we are using a compounded quarterly.
if we said 19.4 then it would not be quarterly it would be monthly
i= 5%= 0.05
then
[tex]F=A(\frac{(1+i)^{n+1}-1}{i}-1[/tex][tex]F=950(\frac{(1+0.05)^{20}-1}{0.05}-1[/tex][tex]F=30462.656[/tex]
the amount F is 30462.656 P
the present value is
[tex]P=A(\frac{1-(1+i)^{n+1}}{i}+1)[/tex][tex]P=950(\frac{1-(1+0.05)^{20}}{0.05}+1)[/tex][tex]P=-30462.656[/tex]
