Question

6. (3pts) A perpetuity paying 100 at the end of each 4-month period has a present value of 5000. What is the present value of an annuity paying 100 at the end of every 3 year for 30 years, assuming the same effective interest rate? (Answer: 426.33) 7 (2nts) There is $10 000 in a fund which is c l etin 40/ -

Math Interest Theory/ Financial Math

Please Use Formulas

Answer 1

Step 1:
Present Value of Perpetuity
PV=A/r-g
PV= Present Value
A= Annuity
r= interest rate
g= growth rate
5000=$100/r-0
=r = 2% ( for every 4 month)
APR = 2*12/4 =6%
Steo 2:
Effective rate of interest for 3 years= (1+r/n)^n -1
n= number of periods
r = interest rate
r =6*3	18.00%
n =36/4	9
= (1+0.18/9) ^9 - 1
=19.51%
Step 3:
c= Cash Flow	100.000
i= Interest Rate	19.5100%
n= Number Of Periods =30/3	10
Present Value Of An Annuity
= C*[1-(1+i)^-n]/i]
Where,
C= Cash Flow per period
i = interest rate per period
n=number of period
= $100[ 1-(1+0.1951)^-10 /0.1951]
= $100[ 1-(1.1951)^-10 /0.1951]
= $100[ (0.8317) ] /0.1951
= $426.33
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