1. (a) How much money will you have accumulated in your bank account if you put
ID: 2551053 • Letter: 1
Question
1. (a) How much money will you have accumulated in your bank account if you put $3,000 in a CD today that earns 4% interest compounded annually for 10 years? (b) What if you could get semiannual compounding of interest on the CD in 1a) 2. (a) How much would you pay today for a zero coupon bond with a face value of $5,000 that yields 6% and matures in 15 years? With a zero coupon bond, you pay today Principal minus interest earned over the period, and receive the face amount at maturity. The Face amount Future Value·You are discounting back to the PV in this problem. This is like us savings bonds or US Treasury bills b) How much interest did you earn over the 15 years? (c) Why are these an attractive investment to a spendthrift and also maybe to an investor who does not have quite as much money to invest? 3. (a) How much money would you have accumulated in a Roth IRA account if you put in $5,000 per year beginning one year from now [an ordinary annuity) and make this contribution for the next 30 years, assuming that you can get an 8% return on your money during that time? (b) What if you begin making the contributions today and at the beginning of every year for the next 30 years (annuity due)? Assume same amount of contribution and interest rate. (c) What is so wonderfull about a Roth IRA rather than a traditional IRA or a 401-K contribution? Hint: The tax break comes at different points.Explanation / Answer
Future value is calculated by compounding the Present cash flow
The formula is,
FV = Present value *(1 + r)^n
= 3000*(1 + 0.04)^10
= 3000*(1.04)^10
= 3000*(1.48024428491834)
= 4440.73
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If the interest is compounded semi annually
FV = Present value *(1 + r)^n
= 3000*(1 + 0.02)^20
= 3000*(1.02)^20
= 3000*(1.48594739597835)
= 4457.84
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Zero coupon bond does not pay any annual coupon, the investor will receive 5000 at the time of maturity.
Present value is the present worth of cash that is to be received in the future, if future value is known, rate of interest in r and time is n then PV is
PV = FV/ (1 + r) ^n
Where,
FV = 5000
r = 0.06
n = 15
Let's put all the values in the formula
= 5000/ (1 + 0.06)^15
= 5000/ (1.06)^15
= 5000/ 2.3966
= 2086.29
Price of the bond is $2086.29
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Interest earned = 5000 – 2086.29 = $2913.71
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Zero coupon bonds trade at tremendous discount, you only have to pay the discounted value and will receive par value at the time of maturity.
That makes it a feasible investment.
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