Question

What is the value today of an investment that pays $900 every 2 years forever starting 1 year from today and $1,800 every two years forever starting two years from today if the APR is 5.25% compounded quarterly? That is, a $900 payment occurs 1 year from today, a $1,800 payment two years from today, a $900 payment 3 years from today, and so on.

Answer 1

Given about an investment,

It pay $900 every 2 year starting 1 year from today and $1800 every 2 years starting 2 years from today

interest rate APR = 5.25% 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+0.0525/4)^8 - 1 = 11.00%

So, PV of series paying $900 every 2 years at year 1 is Periodic payment/periodic rate

=> Value at year 1 = 900/0.11 = $8185.38

So, its value today = (Value at year 1 + Payment at year 1)/(1+quarterly rate/4)^4 = (8185.38+900)/(1+0.0525/4)^4 = $8623.65

For 2nd series, present value now = periodic payment/periodic rate = 1800/0.11 = $16370.76

So, Present value of this investment is sum of PV of both the series = 8623.65 + 16370.76 = $24994