Question

1. Consider a 7-year ordinary annuity that pays $4,000 per month with the first payment made one month from now. If the appropriate discount rate is 12 percent compounded quarterly, what is the value of this annuity 2 years from now? 2. Consider the series of uneven cash flows below: End of Month June JulytSeptember October November Cash Flow$2,300,000 S1,600,000 $2,750,000 3,200,000 $200,000 $7,720,000 If the effective annual rate (EAR) is 4.5 percent, what is the future value of the cash flows at the end of November? 3. A 3 year deferre annuity makes quarterly payments beginning 414 years rom now. f the present value of the annuit is S4,ב 000 and the discount ate S ercent compounded quarterly, what are the quarterly payments? 4. A 10-year 4.8 percent bond makes semiannual interest payments. If the bond currently sells for $942, what is its yield to maturity (YTM)? 5. Diego purchased a 7.4 percent bond which settled on 1/8/2018 and matures on 1/8/2038. If the bond makes semiannual interest payments and currently sells for $1,059, what is its yield to maturity (YTM)?

Answer 1

1.
rate copounded momthly=((1+12%/4)^(4/12)-1)*12=11.882%
Value of the annuity=4000/(11.882%/12)*(1-1/(1+11.882%/12)^60)=180303.1081

2.
rate compounded monthly=((1+4.5%)^(1/12)-1)*12=4.4098%
Value=2300000*(1+4.4098%/12)^5+1600000*(1+4.4098%/12)^4+2750000*(1+4.4098%/12)^3+3200000*(1+4.4098%/12)^2+200000*(1+4.4098%/12)^1+7720000=17890947.26

3.
4598000=x/(1+5.21%/4)^17+x/(1+5.21%/4)^18....=x/(1+5.21%/4)^17*(1-1/(1+5.21%/4)^12)/(1-1/(1+5.21%/4))

Hence, quarterly payments=4598000*(1+5.21%/4)^17/(1-1/(1+5.21%/4)^12)*(1-1/(1+5.21%/4))=512162.9193

4.
=RATE(10*2,4.8%*1000/2,-942,1000)*2
=5.56%

5.
=RATE(20*2,7.4%*1000/2,-1059,1000)*2
=6.85%