Question

What is the value today of an investment that pays $1,800 every two years forever starting one year from today and $3,600 every two years forever starting two years from today if the APR is 7.50% compounded quarterly? That is, a $1,800 payment occurs 1 year from today, a $3,600 payment 2 years from today, a $1,800 payment 3 years from today, and so on.

	$32,841
	$33,706
	$34,570
	$35,434
	$36,298

Answer 1

Given about an investment,

It pay $1800 every 2 year starting 1 year from today and $3600 every 2 years starting 2 years from today

interest rate APR = 7.5% 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+0.075/4)^8 - 1 = 16.02%

So, PV of series paying $1800 every 2 years at year 1 is Periodic payment/periodic rate

=> Value at year 1 = 1800/0.1608 = $11234.44

So, its value today = (Value at year 1 + Payment at year 1)/(1+quarterly rate/4)^4 = (11234.44+1800)/(1+0.075/4)^4 = $12101.01

For 2nd series, present value now = periodic payment/periodic rate = 3600/0.1602 = $22468.87

So, Present value of this investment is sum of PV of both the series = 12101.01 + 22468.87 = $34570

Option C is correct.