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Homework answers / question archive / 1) A zero-coupon bond is a security that pays no interest, and is therefore bought at a substantial discount from its face value
1) A zero-coupon bond is a security that pays no interest, and is therefore bought at a substantial discount from its face value. If stated interest rates are 5% annually (with continuous compounding) how much would you pay today for a zero-coupon bond with a face value of $1,200 that matures in 9 years Please round your answer to the nearest hundredth.
2) A financial institution offers a "double-your-money" savings account in which you will have $2 in 7 years for every dollar you invest today. What stated annual interest rate (assuming monthly compounding) does this account offer? Please round your answer to the nearest hundredth.
3) You have $50,000 in savings for retirement in an investment earning a stated annual rate of 8% compounded semi-annually. You aspire to have $1,000,000 in savings when you retire. Assuming you add no more to your savings, how many years will it take to reach your goal? Please round your answer to the nearest hundredth.
4) You deposit $300 in a bank account that pays 6% stated annual interest compounded quarterly. What is the value of your investment at the end of 10 years? Please round your answer to the nearest hundredth.
1) Computation of Price of Bond with continuous compounding:
Amount = Pe^(rt)
So, P = Amount / e^(rt)
Here,
P = Price of Bond = ?
Amount = Face Value = $1,200
r = Rate = 5%
t = Time = 9 Years
Substituting the values in formula;
P = $1,200/e^(5%*9) = $765.16 or $765
So, You should pay $765 today for a zero-coupon bond with a face value of $1,200 that matures in 9 years.
2) Computation of Interest Rate using Rate Function in Excel:
=rate(nper,pmt,-pv,fv)*12
Here,
Rate = Interest Rate = ?
Nper = 7 years*12 months = 84 months
PMT = 0
PV = $1
FV = $2
Substituting the values in formula:
=rate(84,0,-1,2)*12
Rate or Interest Rate = 9.94%
3) Computation of Number of Years using NPER Function in Excel:
=nper(rate,pmt,-pv,fv)
Here,
NPER = Number of Years = ?
Rate = (1+8%/2)^2 -1 = 8.16%
PMT = 0
PV = $50,000
FV = $1,000,000
Substituting the values in formula:
=nper(8.16%,0,-50000,1000000)
NPER or Number of Years = 38.19 years
So, It will take 38.19 years to reach your goal.
4) Computation of Future Value using FV Function in Excel:
=fv(rate,nper,pmt,-pv)
Here,
FV = Future Value = ?
Rate = 6%/4 = 1.5% compounded quarterly
Nper = 10 years * 4 quarters = 40 quarters
PMT = 0
PV = $300
Substituting the values in formula:
=fv(1.5%,40,0,-300)
FV or Future Value = $544.21
