Question

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

Answer 1

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.