Question

Tina wants to purchase an annuity that should be paid 30 times at the beginning of each year. The nominal APR is 6% ,compound monthly and 3% annual inflation rate. If the present value is $60000.Find the first and last payment.

 

 

Answer 1

 

This is a growing Annuity due as payment is made at Beginning and present value of growing Annuity due is $60000

Apr (r)= 6%

Number of compounding in year(m) = 12

Effective annual rate = ((1+(r/m))^m)-1

((1+(6%/12) )^12)-1

=0.06167781186

Growth rate that is Inflation rate = 3% or 0.03

Number of payment (n)= 30

Present value of growing Annuity due formula =(first Annuity *(1+i)*(1-((1+g)^n/(1+i)^n))/(i-g)

60000= (p*(1+0.06167781186)*(1-((1+0.03)^30/(1+0.06167781186)^30)))/(0.06167781186 -0.03)

60000/20.00746231 = P

P or first Annuity =2998.881071

So first Annuity is 2998.88

Last. Annuity is paid in 30 Years

Years gap from.1st Annuity (n)= 29

Last Annuity or Future Value Formula = First Annuity or PV*(1+g)^n

=2998.881071*(1+3%)^29

=7067.059689

So first Annuity is 2998.88 and last Annuity is 7067.06