What is the value today of an investment that pays $1,600 every two years forever starting one year from today and $3,200 every two years forever starting two years from today if the APR is 7.00% compounded quarterly? That is, a $1,600 payment occurs 1 year from today, a $3,200 payment 2 years from today, a $1,600 payment 3 years from today, and so on.
Question 4 options:
$33,013 

$33,838 

$34,663 

$35,489 

$36,314 
Given about an investment,
It pay $1600 every 2 year starting 1 year from today and $3200 every 2 years starting 2 years from today
interest rate APR = 7% compounded quarterly.
So we first need to calculate 2 year compounded rate
2 year compounded rate can be calculated using formula
2 year compounded rate = (1 + quarterly rate/4)^8  1 = (1+0.07/4)^8  1 = 14.89%
So, PV of series paying $1600 every 2 years at year 1 is Periodic payment/periodic rate
=> Value at year 1 = 1600/0.1489 = $10746.78
So, its value today = (Value at year 1 + Payment at year 1)/(1+quarterly rate/4)^4 = (10746.78+1600)/(1+0.07/4)^4 = $11519.03
For 2nd series, present value now = periodic payment/periodic rate = 3200/0.1489 = $21493.56
So, Present value of this investment is sum of PV of both the series = 11519.03 + 21493.56 = $33013
So, Option A is correct.
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