Young and Company owes bond holders $5,500 interest at the end of each quarter for the next five years. How much must they deposit now at 8% interest compounded quarterly to yield an annuity payment of $5,500?
-- I am pretty sure I know how to do the problem but I am just wondering if it is a future value problem, a present value problem, sinking funds problem or an ammorization problem..?
"How much must they deposit NOW"
isn't that present ?
PV = 5500( 1 - 1.02^-20)/.02
= $89932.88
Yes, that was right. I must have put in the wrong numbers at first when I was doing it so I thought I was using the wrong formula.
Thank you by the way! I appreciate it.
To determine whether it is a future value problem, a present value problem, a sinking funds problem, or an amortization problem, let's break down the information given.
Young and Company owes bond holders $5,500 interest at the end of each quarter for the next five years. This means they need to make a payment of $5,500 every quarter for a total of 20 payments (5 years x 4 quarters per year).
The question asks how much must they deposit now at 8% interest, compounded quarterly, to yield an annuity payment of $5,500.
Based on this information, we can conclude that this is a present value problem. The company needs to determine the amount they need to deposit currently to generate the required annuity payment in the future.
To calculate the present value of an annuity, we can use the present value of an ordinary annuity formula:
PV = PMT * ((1 - (1 + r)^(-n)) / r)
where:
PV = Present value
PMT = Payment per period ($5,500 in this case)
r = Interest rate per period (8% per year = 0.08/4 per quarter)
n = Number of periods (20 quarters in this case)
Plugging in the values into the formula, we get:
PV = $5,500 * ((1 - (1 + 0.08/4)^(-20)) / (0.08/4))
Calculating this expression will give us the amount that Young and Company must deposit currently to yield the desired annuity payment.