Question

an annuity of $10 for 6 years is worth $50 today.

if you have $100 and want to convert it to a 6-year annuity, how much is the annuity?

Answer 1

We need to calculate interest rate based on given information
c= Cash Flow	10
i= Interest Rate	r
n= Number Of Periods	6
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
50= $10[ 1-(1+r)^-6 /r]
5 =[ 1-(1+r)^-6 /r]
r = 0.05471
Interest rate =5.471%
Let us apply this interest rate for second answer
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= $C[ 1-(1+0.05471)^-6 /0.05471]
100= $C[ 1-(1.05471)^-6 /0.05471]
100= $C[ (0.2736) ] /0.05471
C= $20
Annuity = $20