Question

What is the value today of an investment that pays $1,700 every two years forever starting one year from today and $3,400 every two years forever starting two years from today if the APR is 7.25% compounded quarterly? That is, a $1,700 payment occurs 1 year from today, a $3,400 payment 2 years from today, a $1,700 payment 3 years from today, and so on.

a) 31284

b) 32130

c) 32975

d) 33821

e) 34666

Answer 1

Given about an investment,

It pay $1700 every 2 year starting 1 year from today and $3400 every 2 years starting 2 years from today

interest rate APR = 7.25% 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+0.0725/4)^8 - 1 = 15.45%

So, PV of series paying $1700 every 2 years at year 1 is Periodic payment/periodic rate

=> Value at year 1 = 1700/0.15.45 = $11000.42

So, its value today = (Value at year 1 + Payment at year 1)/(1+quarterly rate/4)^4 = (11000.42+1700)/(1+0.0725/4)^4 = $11819.90

For 2nd series, present value now = periodic payment/periodic rate = 3400/0.15.45 = $22000.84

So, Present value of this investment is sum of PV of both the series = 11819.90 + 22000.84 = $33821

Option d is correct.