Question

What is the value today of an investment that pays $1,000 every two years forever starting one year from today and $2,000 every two years forever starting two years from today if the APR is 5.50% compounded quarterly? That is, a $1,000 payment occurs 1 year from today, a $2,000 payment 2 years from today, a $1,000 payment 3 years from today, and so on.

Answer 1

Given about an investment,

It pay $1000 every 2 year starting 1 year from today and $2000 every 2 years starting 2 years from today

interest rate APR = 5.5% 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+0.055/4)^8 - 1 = 11.54%

So, PV of series paying $1000 every 2 years at year 1 is Periodic payment/periodic rate

=> Value at year 1 = 100/0.1154 = $8662.37

So, its value today = (Value at year 1 + Payment at year 1)/(1+quarterly rate/4)^4 = (8662.37+1000)/(1+0.055/4)^4 = $9148.72

For 2nd series, present value now = periodic payment/periodic rate = 2000/0.1154 = $17324.74

So, Present value of this investment is sum of PV of both the series = 9148.72 + 17324.74 = $26473.45