Question

1. A personal account earmarked as a retirement supplement contains $342,100. Suppose $300,000 is used to establish an annuity that earns 5%, compounded quarterly, and pays $5000 at the end of each quarter. How long will it be until the account balance is $0? (Round your answer UP to the nearest quarter.)

2. Find the present value of an annuity due that pays $4000 at the beginning of each quarter for the next 9 years. Assume that money is worth 6.6%, compounded quarterly. (Round your answer to the nearest cent.)

3. Danny Metzger's parents invested $1800 when he was born. This money is to be used for Danny's college education and is to be withdrawn in four equal annual payments beginning when Danny is age 19. Find the amount that will be available each year, if money is worth 6%, compounded annually. (Round your answer to the nearest cent.)

4. As a result of a court settlement, an accident victim is awarded $1.5 million. The attorney takes one-third of this amount, another third is used for immediate expenses, and the remaining third is used to set up an annuity. What amount will this annuity pay at the beginning of each quarter for the next 5 years if the annuity earns 7.7%, compounded quarterly?

(a) Decide whether the problem relates to an ordinary annuity or an annuity due.

(b) Solve the problem. (Round your answer to the nearest cent.)

Answer 1

1. PV of Annuity =300000
Rate per Quarter =5%/4 =1.25%
PMT at end of quarter =5000
Number of Periods using financial Calculator
I/Y =1.25%;PMT=5000;PV=-300000;CPT N
N=111.60 or 112 quarters.

2. Number of Quarters =9*4 =36
PMT =4000
Rate per Quarter =6.6%/4 =1.65%
PV of annuity due =(1+r)*PMT*((1-(1+r)^-n)/r) =(1+1.65%)*4000*((1-(1+1.65%)^-36)/1.65%=109708.78

3. PV of Investment =1800
FV of Investment at year 19 =PV*(1+r)^n =1800*(1+6%)^19 =5446.0791
Number of years of fees=4
The amount available each year =FV of Investment at year 19/((1+r)*(1-(1+r)^-n)/r) =5446.0791/((1+6%)*(1-(1+6%)^-4)/6%)
=1482.73

4. a) It is a case of annuity due
b) Amount available for annuity due =1500000/3 =500000
Rate per quarter =7.7%/4 =1.925%
Number of quarters =5*4 =20
Annuity due =PV/((1+r)*((1-(1+r)^-n)/r) =500000/((1+1.925%)*((1-(1+1.925%)^-20)/1.925%) =29784.14