When a government or corporation sells bonds to raise money, it can do so in one

Question

When a government or corporation sells bonds to raise money, it can do so in one of two ways. It can target a certain amount to raise or it can target a certain amount to pay back at the end of the bond (this is simplified for the purpose of the problem). Let’s examine the two approaches. Suppose the State of Maryland would like to raise money to help pay for the new Purple Line light rail which will connect New Carrollton with Bethesda and is currently planned to run down Campus Drive through campus. Answer the following questions assuming the market rate for zero-coupon bonds that Maryland must pay is 4% per year and it does not pay the bond until the end of the term.

(a) If Maryland seeks to raise $200,000,000 today, how much will it have to pay back in ten years?

(b) Maryland’s state economists look at tax and revenue projections and say that they can only afford to pay back $270,000,000 in ten years. Given that, how much money can they raise today?

You would like to save money to buy a new car that costs $10,000, but currently only have $8,000 and you know you wont have any further excess savings to contribute more to it. You have available to you a fairly good savings account which pays continuously compounded 5% interest rate. Recall that:

X(t + n) = Xt e^(rn)

Using natural logarithms, solve for n to determine how long it will take for the balance of your savings to reach $10,000.

Explanation / Answer

Interest Rate(R) =4%

Year (n) = 10

a.

Amount raised today = $200000000

Amount to be paid in future = amount raised today*(1+R) ^n

Amount to be paid in future =200000000*(1+.04) ^10

Amount to be paid in future =$296048857

b.

If payment of $270,000,000 is afforded in 10 years

Then

Amount to be raised today = pay back afforded in 10 years / (1+R) ^n

Amount to be raised today =270,000,000/ (1+.04) ^10

Amount to be raised today = $182,402,325.58

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