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 payments of $5,500?

To determine the deposit amount needed to yield annuity payments of $5,500, we can use the formula for the Present Value of an Annuity.

The formula is given as:

PV = PMT * (1 - (1 + r)^(-n)) / r

Where:
PV = Present Value (deposit amount)
PMT = Payment amount per period ($5,500)
r = Interest rate per period (8% or 0.08 divided by 4 since it is compounded quarterly)
n = Total number of periods (5 years or 20 quarters)

Now, let's plug in the values and compute the deposit amount needed.

r = 0.08 / 4 = 0.02 (quarterly interest rate)
n = 5 years * 4 quarters = 20 (total number of quarters)

PV = $5,500 * (1 - (1 + 0.02)^(-20)) / 0.02
PV = $5,500 * (1 - (1.02)^(-20)) / 0.02

Using a calculator or computer, we can find that (1.02)^(-20) is approximately 0.6727.

PV ≈ $5,500 * (1 - 0.6727) / 0.02
PV ≈ $5,500 * 0.3273 / 0.02
PV ≈ $90,015

Therefore, Young and Company must deposit approximately $90,015 at 8% interest compounded quarterly to yield annuity payments of $5,500.

To find the amount Young and Company must deposit now, we need to calculate the present value of the annuity payments. The formula to calculate the present value of an annuity is:

PV = PMT * ((1 - (1 + r)^(-n)) / r)

Where:
PV = Present value
PMT = Payment amount per period
r = Interest rate per period
n = Number of periods

In this case, the annuity payment is $5,500, the interest rate is 8% (0.08 as a decimal), compounded quarterly, and there are 20 quarters (5 years * 4 quarters per year).

Plugging in the values into the formula:

PV = $5,500 * ((1 - (1 + 0.08/4)^(-20)) / (0.08/4))

Now we can solve for PV:

PV = $5,500 * ((1 - 1.80364482922) / 0.02)

Simplifying further:

PV = $5,500 * (0.05177758538 / 0.02)

PV = $5,500 * 2.588879269

PV = $14,239.36 (rounded to the nearest cent)

Therefore, Young and Company must deposit approximately $14,239.36 now at an interest rate of 8% compounded quarterly to yield annuity payments of $5,500 every quarter for the next five years.