Question

What is the value today of an investment that pays $2,300 every two years forever starting one year from today and $4,600 every two years forever starting two years from today if the APR is 8.75% compounded quarterly? That is, a $2,300 payment occurs 1 year from today, a $4,600 payment 2 years from today, a $2,300 payment 3 years from today, and so on.
options: $33,847
$34,787
$35,728
$36,668
$37,608

Answer 1

Given about an investment,

It pay $2300 every 2 year starting 1 year from today and $4600 every 2 years starting 2 years from today

interest rate APR = 8.75% 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+0.0875/4)^8 - 1 = 18.90%

So, PV of series paying $2300 every 2 years at year 1 is Periodic payment/periodic rate

=> Value at year 1 = 2300/0.189 = $12169.25

So, its value today = (Value at year 1 + Payment at year 1)/(1+quarterly rate/4)^4 = (12169.25+2300)/(1+0.0875/4)^4 = $13269.51

For 2nd series, present value now = periodic payment/periodic rate = 4600/0.189 = $24338.50

So, Present value of this investment is sum of PV of both the series = 13269.51 + 24338.50 = $37608

Option E is correct.