Question

Exercise A3-17 Present Values Use Present Value Tables or your calculator to complete the requirements below. Required: a. Determine the present value of a single $14,000 cash flow in 7 years if the interest (discount) rate is 8% per year. Round your answer to the nearest cent. $ 8,169 X b. Determine the number of periods for which $5,820 must be invested at an annual interest (discount) rate of 7% to produce an investment balance of $10,000. Round you answer to the nearest whole number of periods. 248 X periods c. Determine the size of the annual cash flow for a 25-year annuity with a present value of $49,113 and an annual interest rate of 9%. One payment is made at the end of each year. Round your answer to the nearest cent. $ 5,000 x d. Determine the annual interest rate at which an investment of $2,542 will provide for a single $4,000 cash flow in 4 years. Round your answer to the nearest whole percentage rate (for example, 10.6% rounds to 11%). 11 X % e. Determine the annual interest rate earned by an annuity that costs $17,119 and provides 15 payments of $2,000 each, one at the end of each of the next 15 years. Rour your answer to the nearest whole percentage rate (for example, 10.6% rounds to 11%). 10 X %

Answer 1

Answer to Question a) Present Value of a single Cash flow = 14,000/(1 + 0.08)^7 = 14000*0.583490 =                       $8,169 (Ans)

Answer to Question b) We know that Future Value (FV) = P V * (1 + r)^n,

Where, r = rate of interest = 7%

                n = No of years or periods.

                PV = Present Value = $ 5,820

                FVF = Future Value Factor

Now, we get, 10000 = 5820 * (1 + 0.07)^n

                    Or, 1.7182 = (1 + 0.07)^n

Now, by looking in to the Future Value FactorTable(or by using calculator), we find out that FVF(7%,8 years) = 1.7182.

Therefore, n = 8 years (approx.) or 96 months (Ans.)

Answer to Question c) Given Present Value of several Cash flows for a 25year annuity = $49,113

Rate of Interest(r) = 9%

No of Years(n) = 25 years

PVAF = Present Value Annuity Factor

Now we got, Present value = Cash Flows * PVAF (r, n)

                        49,113 = Cash Flows * PVAF (9%, 25years)

                        49,113 = Cash Flows *9.82257960421     (PVAF can be calculated in Calculator)

                Therefore, Cash Flows = 49,113/9.82257960421 = $5,000 (Ans)

Answer to Question d) Let Rate of Interest be r

Amount (A) = $4,000

Principal (P) = $2,542

No of years (n) = 4 years

Therefore, by formula of Compounding Interest,

Amount = Principal * (1 + r)^n

Or, 4000 = 2542 * (1 + r)^4

Or, (1 + r)^4 = 4000/2542 = 1.573564

Or, (1 + r) = (1.573564)^1/4 = 1.12

Or, r = 1.12 – 1 = 0.12 or 12% (Ans.)

Answer to Question e) ) Given Present Value of several Cash flows for a 25year annuity = $17,119

Rate of Interest(r) = r

No of Years(n) = 15 years

Annual Cash Flows = $2,000

PVAF = Present Value Annuity Factor

Now we got, Present value = Cash Flows * PVAF (r, n)

                         17,119 = 2,000 * PVAF(r, 15years)

                    Or, PVAF(r, 15years) = 17,119/2,000 = 8.5595

Now, by looking in to the Present Value Annuity Factor Table(or by using calculator), we find out that PVAF(r,15 years) = 8% (Ans.)