Question

4. Find the amount and the present value of an annuity due of P950 every quarter for 6years and 6 months, if money is worth 5% compounded quarterly.The formula is attached

Answer 1

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

`F=A(((1+i)^(n+1)-1)/(i)-1`
`F=950(((1+0.05)^(20)-1)/(0.05)-1`
`F=30462.656`

the amount F is 30462.656 P

the present value is

`P=A((1-(1+i)^(n+1))/(i)+1)`
`P=950((1-(1+0.05)^(20))/(0.05)+1)`
`P=-30462.656`