For each of the following situations involving annuities, solve for the unknown. Assume that interest is compounded annually and that all annuity amounts are received at the end of each period, interest rate, and n number of years EV of $1, PV of $1, EVA of $1 PVA of $1, EVAD of $1 and PVAD of $. Use appropriate factor(s) from the tables provided. Present Value Annuity Amount i = n =1 2,600 8% 52. 507,866 135,000 ___ 43. 661,241 170,000 9% 4. 540,000 78,557 ___ 85. 230,000 10% 4

1) Present Value =  $10,381

2) i = 3%

3) n = 5  

4) i = 4%

5) Annuity amount = $72,558

Explanation:

Given that;

No.       Present Value       Annuity Amount         i =                n =

1.                                2,600                       8%               5

2.             507,866                 135,000                     ___             4

3.              661,241                  170,000                     9%             ___

4.              540,000                 78,557                      ___             8

5.              230,000                                         10%              4

Assume that interest is compounded annually and that all annuity amounts are received at the end of each period, interest rate, and n number of years EV of $1, PV of $1, EVA of $1 PVA of $1, EVAD of $1 and PVAD of $.

we know that

Present value = Annuity amount × Discount factor at i% for n years

1) Present value = 2600 × Discount factor at 8% for 5 years  

from the annuity table ( n = 5, i =8% :- 3.99271)

Present Value = 2600 × 3.99271 = $10,381

2) 507,866 = 135,000 × Discount factor at i% for 4 years  

Discount factor at i% for 4 years = 507,866 / 135,000  

Discount factor at i% for 4 years =  3.761970

Check Present value annuity table in period 4 row for 3.761970

i = 3%

3)  661,241 = 170,000 × Discount factor at 9% for n years  

Discount factor at 9% for n years =661,241 / 170,000  

Discount factor at 9% for n years = 3.88965  

Check Present value annuity table in 9% column for 3.88965

n = 5  

4) 540,000 =  78,557 × Discount factor at i% for 8 years  

Discount factor at i% for 8 years = 540,000 / 78,557  

Discount factor at i% for 8 years = 6.8739895  

Check Present value annuity table in period 8 row for 6.8739895  

i = 4%

5) 230,000  = Annuity amount × Discount factor at 10% for 4 years

from the annuity table ( n = 4, i =10% :- 3.169865)

230,000  = Annuity amount × 3.169865  

Annuity amount =  230,000 / 3.169865 = $72,558

explanation:

start by isolating the variable on one side by adding 43w^2 to both sides.   the equation will read:

25w^2+5=0

*subtract 5 from both sides*

25w^2=-5

*divide both sides by 25*

w^2=-1/5

*take the square root of both sides*

w=√(-1/5)

the square root of -1 is i.   the square root of 5 remains √5

the answer is i/√5.

hope this