Practical applications of the time value of money
- a. How much would you have to deposit today if you wanted to have $60,000 in four years? Annual interest rate is 9%.
- b. Assume that you are saving up for a trip around the world when you graduate in two years. If you can earn 8% on your investments, how much would you have to deposit today to have $15,000 when you graduate?
- c. Would you rather have $463 now or $1,000 ten years from now? Assume that you can earn 9% on your investments.
- d. Assume that a college parking sticker today costs $90. If the cost of parking is increasing at the rate of 5% per year, how much will the college parking sticker cost in eight years?
- e. Assume that the average price of a new home is $158,500. If the cost of a new home is increasing at a rate of 10% per year, how much will a new home cost in eight years?
- f. An investment will pay you $10,000 in 10 years and it will also pay you $400 at the end of each of the next 10 years (years 1 thru 10). If the annual interest rate is 6%, how much would you be willing to pay today for this type of investment?
- g. A college student is reported in the newspaper as having won $10,000,000 in the Kansas State Lottery. However, as is often the custom with lotteries, she does not actually receive the entire $10 million now. Instead she will receive $500,000 at the end of the year for each of the next 20 years. If the annual interest rate is 6%, what is the present value (today’s amount) that she won? (Ignore taxes.)
a.
Calculate the amount that is to be deposited today to receive $60,000 in four years.
Explanation of Solution
Present Value:
Present value refers to the current value of future sum of money in lump sum or in instalments with a stated rate of interest.
Therefore, the present value of the amount that is to be deposited today to receive $60,000 in four years is $42,504.
b.
Calculate the amount that is to be deposited today to receive $15,000 while graduating.
Explanation of Solution
Present Value:
Present value refers to the current value of future sum of money in lump sum or in instalments with a stated rate of interest.
Therefore, the present value of the amount that is to be deposited today to receive $15,000 while graduating is $12,859.60.
c.
Identify whether $463 currently or $1,000 will be received after 10 years from now.
Explanation of Solution
Future value:
The future value is value of present amount compounded at an interest rate until a particular future date.
Present Value:
Present value refers to the current value of future sum of money in lump sum or in instalments with a stated rate of interest.
Calculate the future value of $463 at 9% for 10 years:
Therefore, the future value of $463 is $1,096.12.
Calculate the present value of $1,000 will be received after 10 years from now:
Therefore, the present value of $1,000 will be received after 10 years from now is $422.40
d.
Calculate the cost of college parking sticker in eight years.
Explanation of Solution
Future value:
The future value is value of present amount compounded at an interest rate until a particular future date.
Calculate the cost of college parking sticker in eight years:
Therefore, the cost of college parking sticker in eight years is $132.98.
e.
Calculate the cost of new home in eight years.
Explanation of Solution
Future value:
The future value is value of present amount compounded at an interest rate until a particular future date.
Calculate the cost of new home in eight years.
Therefore, the cost of new home in eight years is $339,764.20.
f.
Calculate the amount that will be paid today for given type of investment in this situation.
Explanation of Solution
Present Value:
Present value refers to the current value of future sum of money in lump sum or in instalments with a stated rate of interest.
Annuity:
An annuity is referred as a sequence of payment of fixed amount of cash flows that occurs over the equal intervals of time.
Calculate the amount that will be paid today for given type of investment in this situation by using a present value of a lump sum part:
Calculate the amount that will be paid today for given type of investment in this situation by using a present value of an annuity part:
Therefore, the amount that will be paid today for given type of investment in this situation is
g.
Calculate the present value for the given transaction.
Explanation of Solution
Present Value:
Present value refers to the current value of future sum of money in lump sum or in instalments with a stated rate of interest.
Annuity:
An annuity is referred as a sequence of payment of fixed amount of cash flows that occurs over the equal intervals of time.
Calculate the present value:
Therefore, the present value is $5,734,950.
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Chapter B Solutions
Principles of Financial Accounting.
- Use the tables in Appendix B to answer the following questions. A. If you would like to accumulate $4,200 over the next 6 years when the interest rate is 8%, how much do you need to deposit in the account? B. If you place $8,700 in a savings account, how much will you have at the end of 12 years with an interest rate of 8%? C. You invest $2,000 per year, at the end of the year, for 20 years at 10% interest. How much will you have at the end of 20 years? D. You win the lottery and can either receive $500,000 as a lump sum or $60,000 per year for 20 years. Assuming you can earn 3% interest, which do you recommend and why?arrow_forwardCalculating interest earned and future value of savings account. If you put 6,000 in a savings account that pays interest at the rate of 3 percent, compounded annually, how much will you have in five years? (Hint: Use the future value formula.) How much interest will you earn during the five years? If you put 6,000 each year into a savings account that pays interest at the rate of 4 percent a year, how much would you have after five years?arrow_forwardYou put $250 in the bank for S years at 12%. A. If interest is added at the end of the year, how much will you have in the bank after one year? Calculate the amount you will have in the bank at the end of year two and continue to calculate all the way to the end of the fifth year. B. Use the future value of $1 table in Appendix B and verity that your answer is correct.arrow_forward
- You hope to have $35,000 in your investment account in ten years. If you invest $25,000 today, what annual rate of return would your investment account need to generate if you make no future deposits? Group of answer choices 3.4% 3.8% 40.0% 1.7%arrow_forwardYou plan to invest $5,000 into an account. If you would like to have $10,000 in 15 years, what rate of return must you earn? Question 5 options: 6.02% 5.24% 4.73% 7.55% 7.11%arrow_forwardAssume that you are saving up for a trip around the world when you graduate in two years. If you can earn 8% on your investments, how much would you have to deposit today to have $15,000 when you graduate?arrow_forward
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- Suppose you have $10,000 to invest for the next 30 years. You are given 3 choices on where to invest your money. Account #1 Account #2 Account #3 a. Calculate the APR (assume P-$100, -1 year) for each account. Round to 2 decimal places, in percent form. Account #1 15.21% compounded monthly 15.18% compounded daily 15.16% compounded continuously SHOW YOUR WORK BELOW.arrow_forwardHow much should you invest each month in order to have $300,000 if your rate of return is 5.6% compounded monthly and you want to achieve your goal in 40 years? $ How much interest will you earn? $ How much should you invest each month in order to have $300,000 if you want to achieve your goal in 20 years? $ If you deposit the amount you need to achieve your goal in 20 years, how much will your savings be worth after 10 years? $ esarrow_forward(Use Calculator or Formula Approach) Suppose you need $15,000 in 3 years . If you can earn 6% annually, how much do you need to invest today? If you could invest the money at 8%, would you have to invest more or less than at 6%? How much?0arrow_forward
- Principles of Accounting Volume 2AccountingISBN:9781947172609Author:OpenStaxPublisher:OpenStax CollegePfin (with Mindtap, 1 Term Printed Access Card) (...FinanceISBN:9780357033609Author:Randall Billingsley, Lawrence J. Gitman, Michael D. JoehnkPublisher:Cengage Learning