To think critically about: The relationship between the value of an
Introduction:
The total sum of interest that is due for a particular time is the interest rate. The rate of interest can be due for a period as a proportion of the sum borrowed or deposited and as the proportion of the sum lent. The future sum of money that is worth today is described by the
Explanation of Solution
The relationship between the interest rate and the
- If the interest rate maximizes, the present value of the annuity would decrease and the present value of annuity would increase if the interest rate decreases.
- If the rate of interest increases, the
future value of the annuity would increase and the future value of annuity would decrease if the interest rate decreases.
To calculate: The present value of
Introduction:
The total sum of interest that is due for a particular time is the interest rate. The rate of interest can be due for a period as a proportion of the sum borrowed or deposited and as the proportion of the sum lent. The future sum of money that is worth today is described by the present value. The present value of the cash flows in the future with a particular discount rate is the present value of annuity.
Answer:
- The present value of annuity with an interest rate of 10% is $44,855.34.
- The present value of annuity with an interest rate of 5% is $56,368.66.
- The present value of annuity with an interest rate of 15% is $36,637.01.
Answer to Problem 38QP
- The present value of
annuity with an interest rate of 10% is $44,855.34. - The present value of annuity with an interest rate of 5% is $56,368.66.
- The present value of annuity with an interest rate of 15% is $36,637.01.
Explanation of Solution
Given information:
Person X purchased a ten-year
Time line:
Formula to calculate the present value of annuity:
Note: C denotes the annual cash flow, r denotes the rate of exchange, and t denotes the period.
Compute the present value of annuity at 10% interest:
Hence, the present value of annuity at 10% is $44,855.34.
Compute the present value of annuity at 5% interest:
Hence, the present value of annuity at 5% is $56,368.66.
Compute the present value of annuity at 15% interest:
Hence, the present value of annuity at 15% is $36,637.01097.
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Chapter 5 Solutions
Essentials of Corporate Finance (Mcgraw-hill/Irwin Series in Finance, Insurance, and Real Estate)
- Suppose you are going to receive $13,500 per year for five years. The interest rate is 8.4%a. What is the present value of the payments if they are in the form of an ordinary annuity? What is the present value if the payments are an annuity due?b. Suppose you plan to invest the payments for five years. What is the future value if the payments are an ordinary annuity? What if the payments are annuity due?c. Which has the highest present value (future value), the ordinary annuity or annuity due?arrow_forwardthe discount rate or the interest rate increases for a given time period? As the discount rate or the interest rate decreases? 10. Relationship between an ordinary annuity and an annuity due. Compare the present value of a $6,000 ordinary annuity at 10 percent interest for ten years with the present value of a $6,000 annuity due at 10 percent interest for eleven years. Explain the difference.arrow_forwardThe present value of an annuity is the sum of the discounted value of all future cash flows. You have the opportunity to invest in several annuities. Which of the following 10-year annuities has the greatest present value (PV)? Assume that all annuities earn the same positive interest rate. An annuity that pays $500 at the end of every six months An annuity that pays $1,000 at the end of each year An annuity that pays $1,000 at the beginning of each year*** This is the correct option**** An annuity that pays $500 at the beginning of every six months A. An ordinary annuity selling at $2,514.15 today promises to make equal payments at the end of each year for the next eight years (N). If the annuity’s appropriate interest rate (I) remains at 8.00% during this time, the annual annuity payment (PMT) will be . B. You just won the lottery. Congratulations! The jackpot is $10,000,000, paid in eight equal annual payments. The…arrow_forward
- The amount of money originally put into an investment is known as the present value P of the investment. For example, if you buy a $50 U.S. Savings Bond that matures in 10 years, the present value of the investment is the amount of money you have to pay for the bond today. The value of the investment at some future time is known as the future value F. Thus, if you buy the savings bond mentioned above, its future value is $50. If the investment pays an interest rate of r (as a decimal) compounded yearly, and if we know the future value F for t years in the future, then the present value P = P(F, r, t), the amount we have to pay today, can be calculated using the formula below. P = F × 1 (1 + r)t We measure F and P in dollars. The term 1/(1 + r)t is known as the present value factor, or the discount rate, so the formula above can also be written as the following. P = F × discount rate (a) Explain what information the function P(F, r, t) gives you. The function…arrow_forwardThe present value of an annuity is the sum of the discounted value of all future cash flows. You have the opportunity to invest in several annuities. Which of the following 10-year annuities has the greatest present value (PV)? Assume that all annuities earn the same positive interest rate. O An annuity that pays $500 at the end of every six months An annuity that pays $500 at the beginning of every six months An annuity that pays $1,000 at the end of each year. An annuity that pays $1,000 at the beginning of each year An ordinary annuity selling at $14,130.15 today promises to make equal payments at the end of each year for the next twelve years (N). If the annuity's appropriate interest rate (I) remains at 8.00% during this time, the annual annuity payment (PMT) will be You just won the lottery. Congratulations! The jackpot is $85,000,000, paid in twelve equal annual payments. The first payment on the lottery jackpot will be made today. In present value terms, you really won…arrow_forwardSuppose you are going to receive Rs. 63,800 per year for five years. The appropriate interest rate is 7.3 What is the present value of the payments if they are in the form of an ordinary annuity? What is the present value if the payments are an annuity due? Suppose you plan to invest the payments for five years. What is the future value if the payments are an ordinary annuity? What if the payments are an annuity due? Which has the highest present value, the ordinary annuity or annuity due? Which has the highest future value? Will this always be true? Note- Answer all the parts of the questionarrow_forward
- The present value of an annuity is the sum of the discounted value of all future cash flows. You have the opportunity to invest in several annuities. Which of the following 10-year annuities has the greatest present value (PV)? Assume that all annuities earn the same positive interest rate. O An annuity that pays $500 at the beginning of every six months O An annuity that pays $500 at the end of every six months O An annuity that pays $1,000 at the beginning of each year O An annuity that pays $1,000 at the end of each year An ordinary annuity selling at $4,947.11 today promises to make equal payments at the end of each year for the next eight years (N). If the annuity's appropriate interest rate (1) remains at 6.50% during this time, the annual annuity payment (PMT) will be You just won the lottery. Congratulations! The jackpot is $35,000,000, paid in eight equal annual payı The first payment on the lottery jackpot will be made today. In present value terms, you really won -assuming…arrow_forwardSuppose you just bought an annuity with 10 annual payments of $16,500 at a discount rate of 13.75 percent per year. a. What is the value of the investment at the current interest rate of 13.75 percent? Note: Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16. b. What happens to the value of your investment if interest rates suddenly drop to 8.75 percent? Note: Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16. c. What happens to the value of your investment if interest rates suddenly rise to 18.75 percent? Note: Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.arrow_forwardSuppose you just bought an annuity with 12 annual payments of $15,700 at a discount rate of 11.75 percent per year. a. What is the value of the investment at the current interest rate of 11.75 percent? Note: Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16. b. What happens to the value of your investment if interest rates suddenly drop to 6.75 percent? Note: Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16. c. What happens to the value of your investment if interest rates suddenly rise to 16.75 percent? Note: Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16. a. Present value at 11.75 percent b. Present value at 6.75 percent $ 124,187.88 153,795.59 c. Present value at 16.75 percent $ 97,472.81arrow_forward
- Suppose you are going to receive $13,000 per year for 7 years. The appropriate interest rate is 8 percent. a.What is the present value of the payments if they are in the form of an ordinary annuity? b.What is the present value if the payments are an annuity due? c.Suppose you plan to invest the payments for 7 years, what is the future value if the payments are an ordinary annuity? d.Suppose you plan to invest the payments for 7 years, what is the future value if the payments are an annuity due?arrow_forwardSuppose you're going to receive $7800 per year for five years. the appropriate discount rate is 7.5%. A.What is the present value of the payments if they are in the form of an ordinary annuity? What is the present value if the payments are an annuity due? B. Suppose you plan to invest the payments for five years. What is the future value if the payments are an ordinary annuity? What if the payments are in annuity due? C. Which has the higher present value, the ordinary annuity or the annuity due? Which has a higher future value? Will this always be true?arrow_forwardSuppose you just bought an annuity with 11 annual payments of $16,400 at a discount rate of 13.5 percent per year. What is the value of the investment at the current interest rate of 13.5 percent? Note: Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16. What happens to the value of your investment if interest rates suddenly drop to 8.5 percent? Note: Do not round intermediate calculations and roundarrow_forward