Seanna O'Brien receives pension payments of $1,610 at the end of every three months from a...
Seanna O'Brien receives pension payments of $1,610 at the end of every three months from a retirement fund of $52,000. The fund earns 11% compounded quarterly.
(a) How many payments will Seanna receive?
(b) What is the size of the final pension payment?
Homework Answers
Qa:
This is an annuity problem and where Present value of annuity=52000
PV of annuity= A[1-(1+r)^-n]/r
where A=annuity payment ;r= interest rate quarterly= 11/4=2.75%
n= no of quarters=?
52000=1610*[1-(1+2.75%)^-n]/.0275
By equating the values or using trial and error;
n= 80.8 = 81 payments (appx)
Qb:
Size of the final pension payment; we need to find future value of annuity payement
FV of annuity =A*[(1+r)^n-1]/r
=1610*[(1+2.75%)^81 -1]/.0275
=468467.70
----
PV of annuity taking n=81; PV=52041.68
ie; in last term only 1610-41.68 =1568.32 has to be paid.
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