Question

What is the value today of an investment that pays $2,700 every two years forever starting one year from today and $5,400 every two years forever starting two years from today if the APR is 9.75% compounded quarterly? That is, a $2,700 payment occurs 1 year from today, a $5,400 payment 2 years from today, a $2,700 payment 3 years from today, and so on.

Answer 1

Given about an investment,

It pay $2700 every 2 year starting 1 year from today and $5400 every 2 years starting 2 years from today

interest rate APR = 9.75% 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+0.0975/4)^8 - 1 = 21.25%

So, PV of series paying $2700 every 2 years at year 1 is Periodic payment/periodic rate

=> Value at year 1 = 2700/0.2125 = $12707.55

So, its value today = (Value at year 1 + Payment at year 1)/(1+quarterly rate/4)^4 = (12707.55+2700)/(1+0.0975/4)^4 = $13992.58

For 2nd series, present value now = periodic payment/periodic rate = 5400/0.2125 = $25415.10

So, Present value of this investment is sum of PV of both the series = 13992.58 + 25415.10 = $39408