how much should rod pay for a 10 year annuity that provides month end payments of 1800 at 4.5% compounded quarterly
P= N [ 1 - (1+r)^-n ] /r
P = present value, what he pays
N = payment amount
r = interest rate/period
n = number of payments
here n = 120 months
need compound interest rate per month, not quarterly
.045/4 = .01125
1.01125^4 = 1.045765 per year
(1+r)^12 = 1.045765
(1+r) = 1.003736
so monthly interest rate r = .003736
we have
P = 1800 [ 1 - 1.003736^-120 ]/.003736
= 1800 [ 1 - .63923 ]/.003736
= 1800 ( .360768/.003736 ]
= $ 173,817.48