# Math Help - Present value of an ordinary simple annuity

1. ## Present value of an ordinary simple annuity

Francois and pat wish to structure the payments from a 20-year annuity so that the end of quarter paments increase by $500 every five years. Maritime insurance co will pay 5% compounded quarterly on funds recived to purchase such an annuity. How much must francois and pat pay for an annuity in which the quarterly payments increase from$2000 to 2500 to 3000 to 3500 in successive five year periods?

PV = PMT (( 1 - ( 1 + i )^n / i ) +
FV = PV ( 1 + i )

i = 0.05/4

n = 4 ( 5? ) or 20 ? confused on that

PMT = 2000 ? confused on that also

2. Question simply worded:
\$x is deposited in an account paying 5% compounded quarterly,
such that these 80 quarterly payments will be possible:
2000 for 1st 5 years
2500 for next 5 years
3000 for next 5 years
3500 for last 5 years.

Let = 1 - 1 / 1.0125^20
a = 2000f
b = 2500f / 1.0125^20
c = 3000f / 1.0125^40
d = 3500f / 1.0125^60

x = a + b + c + d ; ~130872.88

Couple questions for you:
where are these problems coming from?
are you attending classes for these?