Question

What is the value today of an investment that pays $2,500 every two years forever starting one year from today and $5,000 every two years forever starting two years from today if the APR is 9.25% compounded quarterly? That is, a $2,500 payment occurs 1 year from today, a $5,000 payment 2 years from today, a $2,500 payment 3 years from today, and so on.

Answer 1

Given about an investment,

It pay $2500 every 2 year starting 1 year from today and $5000 every 2 years starting 2 years from today

interest rate APR = 9.25% 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+0.0925/4)^8 - 1 = 20.07%

So, PV of series paying $2500 every 2 years at year 1 is Periodic payment/periodic rate

=> Value at year 1 = 2500/0.2007 = $12457.25

So, its value today = (Value at year 1 + Payment at year 1)/(1+quarterly rate/4)^4 = (12457.25+2500)/(1+0.0925/4)^4 = $13650.14

For 2nd series, present value now = periodic payment/periodic rate = 5000/0.2007 = $24914.50

So, Present value of this investment is sum of PV of both the series = 13650.14 + 24914.50 = $38565