Question

Finance problems thx!

4. Consider the following securities: (i) an annuity that pays $1,000 a year at the end of each of the next 10 years, (ii) a perpetuity that pays $1,000 a year forever starting 11 years from today. a. What are the values of these securities at an annual interest rate of 4%? b. What are the values of these securities at an annual interest rate of 10%?

Answer 1

SEE THE IMAGE. ANY DOUBTS, FEEL FREE TO ASK. THUMBS UP PLEASE

PERPETUITY STARTS FROM END OF 11TH YEAR, SO WE HAVE TO DISCOUNT IT FOR 10 YEARS TO GET VALUE AS OF TODAY

PV = PV OF PERTUITY X PVIF @ RATE, NO OF YEARS

W v . * 05:33 ENG 23-02-202013 Q1 I fix R P Q S T U V W X Y Z AA AB AC AD E a RATE = 4% PRESENT VALUE OF ANNUITY PV = PMT X PVIFA @4%, 10 YEARS PV = 1000 X (1/r)*(1-(1/(1+r)^n)) PV = 1000 X (1/0.04)*(1-(1/(1+0.04)^10)) PV = 8110.90 PRESENT VALUE OF PERPETUITY PV = PV OF PERPETUITY X PVIF @ 4%, 10 YEARS PV = (A/r) X (1/(1+r)^n) PV = (1000/0.04) X (1/(1+0.04) 10 PV = 16889.10 ... FV EXCEL PV EXCEL Sheet1 Sheet2 ASSETL UTILITY LOAN EAIR OLIVER RETIRE USE EXCEL gnp DOLLA ... :

05:33 W v 4 ENG 23-02-202013 041 . P fix R Q S T U V W X Y Z AA A AC AD E a b RATE = 10% PRESENT VALUE OF ANNUITY PV = PMT X PVIFA @10%, 10 YEARS PV = 1000 X (1/r)*(1-(1/(1+r)^n)) PV = 1000 X (1/0.10)*(1-(1/(1+0.10)^10)) PV = 6144.57 PRESENT VALUE OF PERPETUITY PV = PV OF PERPETUITY X PVIF @ 10%, 10 YEARS PV = (A/r) X (1/(1+r)^n) PV = (1000/0.10) x (1/(1+0.10) 10 PV = 3855.43 ... FV EXCEL PV EXCEL Sheet1 Sheet2 ASSETL UTILITY LOAN EAIR OLIVER RETIRE USE EXCEL gnp DOLLA ... :