Question

For each of the following situations involving annulties, solve for the unknown. Assume that Interest is compounded annually and that all annuity amounts are recelved at the end of each perlod. ( = 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 $1) (Use appropriate factor(s) from the tables provided. Round your final answers to nearest whole dollar amount.) Annuity Amount Present Value евоок 1. 2,000 8% 585,296 150,000 References 200,000 9% 13. 351,822 69,620 18 4. 510,000 14 10% 245,000 00

Answer 1

Present value is the value today of a future sum of cash. Annuity is a series of equal cash payments made at equal intervals. Ordinary annuity is an annuity in which first cash payment is not made today but after the completion of first interval period. Thus, the present value of ordinary annuity refers to value today of series of equal cash payments made at equal intervals.
For this question, present value of annuity table is referred.

1. Annuity amount = $2,000, i = 8%, n = 5

In the table factor for 8% interest and n as 5 years is 3.99271

Present value = Annuity amount * 3.99271 = $7,985.42

2. Present value = $585,296 , Annuity amount = $150,000 n = 4

Present Value = Annuity amount * PVOA factor

PVOA factor = Present value/ Annuity amount = $585,296/$150,000 = 3.90197

In the table, with n as 4 years, PVOA factor is 3.90197 at i = 1%

3. Present value = $351,822, Annuity amount = $200,000, i = 9%

Present Value = Annuity amount * PVOA factor

PVOA factor = Present value/ Annuity amount = $351,822/200,000 = 1.75911

In the table with i as 9%, PVOA factor is 1.75911 at n = 2

4. Present value = $510,000 Annuity amount = $69,620, n = 8

Present Value = Annuity amount * PVOA factor

PVOA factor = Present value/ Annuity amount = $510,000/69,620 = 7.32548

In the table with n as 8 years, PVOA factor is 7.32548 at i = 2%

5. Present value = $245,000, i = 10%, n = 4

Present Value = Annuity amount * PVOA factor

Annuity amount = Present value/PVOA factor = $245,000/3.1699 = $77,289.50