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Homework answers / question archive / 1) Mary Mills has retired after 35 years with the Electric Company her total pension funds have an accumulated value of $300,000, and her life expectancy is 18 more years
1) Mary Mills has retired after 35 years with the Electric Company her total pension funds have an accumulated value of $300,000, and her life expectancy is 18 more years. Her pension fund manager assumes that she can earn an 8 percent return on her assets. What will her yearly annuity be for the next 18 years?
a) If investors are to earn a 4 percent real interest rate, what nominal interest rate must they earn if the inflation rate is:
b) Perpetuities. A property will provide $10,000 a year forever. If its value is $125,000, what must be the discount rate
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1) Computation of Yearly Annuity using PMT Function in Excel:
=pmt(rate,nper,-pv,fv)
Here,
PMT = Yearly Annuity = ?
Rate = 8%
Nper = 18 years
PV = $300,000
FV = 0
Substituting the values in formula:
=pmt(8%,18,-300000,0)
PMT or Yearly Annuity = $32,010.63
2) Computation of Nominal Interest Rate:
Real Interest Rate = [(1+Nominal Interest Rate)/(1+Inflation Rate)] - 1
a) If the inflation rate is zero:
4% = [(1+Nominal Interest Rate)/(1+0)] - 1
4% + 1 = 1+Nominal Interest Rate
4% = 1+Nominal Interest Rate - 1
Nominal Interest Rate = 4%
b) If the inflation rate is 4%:
4% = [(1+Nominal Interest Rate)/(1+4%)] - 1
4% + 1 = (1+Nominal Interest Rate)/1.04
(4%+1)*1.04 = 1+Nominal Interest Rate
0.0416 + 1.04 = 1+Nominal Interest Rate
1+Nominal Interest Rate = 1.0816
Nominal Interest Rate = 1.0816 - 1
Nominal Interest Rate = 8.16%
c) If the inflation rate is 6%:
4% = [(1+Nominal Interest Rate)/(1+6%)] - 1
4% + 1 = (1+Nominal Interest Rate)/1.06
(4%+1)*1.06 = 1+Nominal Interest Rate
0.0424 + 1.06 = 1+Nominal Interest Rate
1+Nominal Interest Rate = 1.1024
Nominal Interest Rate = 1.1024 - 1
Nominal Interest Rate = 10.24%
3) Computation of Discount Rate:
Present Value of Perpetuity = Cash Flow/Discount Rate
$125,000 = $10,000/Discount Rate
Discount Rate = $10,000/$125,000 = 8%
