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.

What is the value today of an investment that pays $900 every
two years forever starting one 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 2 years from today, a $900 payment 3 years
from today, and so on.

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.

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.

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.

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.

What is the value today of an investment that pays $1,800 every
two years forever starting one year from today and $3,600 every two
years forever starting two years from today if the APR is 7.50%
compounded quarterly? That is, a $1,800 payment occurs 1 year from
today, a $3,600 payment 2 years from today, a $1,800 payment 3
years from today, and so on.
$32,841
$33,706
$34,570
$35,434
$36,298

What is the value today of an investment that pays $2,300 every
two years forever starting one year from today and $4,600 every two
years forever starting two years from today if the APR is 8.75%
compounded quarterly? That is, a $2,300 payment occurs 1 year from
today, a $4,600 payment 2 years from today, a $2,300 payment 3
years from today, and so on.
options: $33,847
$34,787
$35,728
$36,668
$37,608

What is the value today of an investment that pays $2,000 every
two years forever starting one year from today and $4,000 every two
years forever starting two years from today if the APR is 8.00%
compounded quarterly? That is, a $2,000 payment occurs 1 year from
today, a $4,000 payment 2 years from today, a $2,000 payment 3
years from today, and so on.
$35,016
$35,913
$36,811
$37,709
$38,607

What is the value today of an investment that pays $1,600 every
two years forever starting one year from today and $3,200 every two
years forever starting two years from today if the APR is 7.00%
compounded quarterly? That is, a $1,600 payment occurs 1 year from
today, a $3,200 payment 2 years from today, a $1,600 payment 3
years from today, and so on.
Question 4 options:
$33,013
$33,838
$34,663
$35,489
$36,314

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.

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