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Mathematical Applications for the ...

12th Edition
Ronald J. Harshbarger + 1 other
Publisher: Cengage Learning
ISBN: 9781337625340

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BuyFindarrow_forward

Mathematical Applications for the ...

12th Edition
Ronald J. Harshbarger + 1 other
Publisher: Cengage Learning
ISBN: 9781337625340
Chapter 6.4, Problem 54E
Textbook Problem
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A couple received a $134,000 inheritance the year they turned 48 and invested it in a fund that earns 7.7% compounded semiannually. If this amount is deferred for 14 years (until they retire), how much will it provide at the end of each half-year for the next 20 years after they retire?

To determine

To calculate: The amount that is provided at the end of each half-year to the couple after they retire, if an inheritance of $134,000 is received by a couple after they turned 48.

Explanation of Solution

Given Information:

An inheritance of $134,000 is received by a couple after they turned 48. They invest it in a fund earning 7.7% compounded semiannually for the next 20 years after they retire. The amount has been deferred for 14 years.

Formula used:

The present value of a deferred annuity of $R per period for n number of periods, deferred for k number of periods with rate of interest i per period is,

A(n,k)=R[1(1+i)ni](1+i)k

Calculation:

Consider the provided information:

An inheritance of $134,000 is received by a couple after they turned 48. They invest it in a fund earning 7.7% compounded semiannually for the next 20 years after they retire. The amount has been deferred for 14 years.

According to the information,

An inheritance of $134,000 is received by a couple.

Hence A(n,k)=134,000.

And the amount is invested for the next 20 years,

n=20×2=40

Since, it is after a deferred payment of 14 years,

k=14×2=28

They are at 7.7% compounded semiannually.

i=7.7100×12=0.0385

The present value of the deferred due will be:

A(n,k)=R[1(1+i)ni](1+i)k

Substitute 134,000 for A(n,k), 0

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Chapter 6 Solutions

Mathematical Applications for the Management, Life, and Social Sciences
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Comparing yields Find the annual percentage...Ch. 6 - 24. Chess legend Legend has it that when the king...Ch. 6 - 25. Chess legend If in Problem 24 the king granted...Ch. 6 - 26. Annuity Find the future value of an ordinary...Ch. 6 - 27. Sinking fund How much would have to be...Ch. 6 - 28. Annuity Find the future value of an annuity...Ch. 6 - 29. Construction fund A company wants to have...Ch. 6 - 30. Time to reach a goal If $1200 is deposited at...Ch. 6 - 31. Annuity What lump sum would have to be...Ch. 6 - 32. Cruise fund A couple want to set up an annuity...Ch. 6 - 33. Powerball lottery Winners of lotteries receive...Ch. 6 - 34. Payment from an annuity A recent college...Ch. 6 - 35. Payment from an annuity An IRA of $250,000 is...Ch. 6 - 36. Bond pricing Suppose that a 30-year municipal...Ch. 6 - 37. Duration of an annuity A retirement account...Ch. 6 - 38. Amortization A debt of $1000 with interest at...Ch. 6 - 39. Loan payoff A debt of $8000 is amortized with...Ch. 6 - 40. Cash value A woman paid $90,000 down for a...Ch. 6 - 41. Amortization schedule Complete the...Ch. 6 - 42. Loan refinancing A corporation borrowed...Ch. 6 - Identify which of the following formulas applies...Ch. 6 - Identify which of the following formulas applies...Ch. 6 - Identify which of the following formulas applies...Ch. 6 - Identify which of the following formulas applies...Ch. 6 - Identify which of the following formulas applies...Ch. 6 - Identify which of the following formulas applies...Ch. 6 - 49. If an initial investment of $2500 grows to...Ch. 6 - 50. How much must be deposited at the end of each...Ch. 6 - 51. What is the future value if $1000 is invested...Ch. 6 - 52. Quarterly payments of $500 are deposited in an...Ch. 6 - 53. If $8000 is invested at 7% compounded...Ch. 6 - 54. An investment broker bought some stock at...Ch. 6 - 55. A couple believes they can afford a monthly...Ch. 6 - 56. A $5000 Mauranol, Inc., corporate bond matures...Ch. 6 - 57. Kevin Patrick paid off the loan he took out to...Ch. 6 - 58. A young couple receive an inheritance of...Ch. 6 - 59. A banker is trying to decide whether to...Ch. 6 - 60. To purchase a home, a couple borrowed $280,000...Ch. 6 - 61. A divorce settlement of $40,000 is paid in...Ch. 6 - 62. If $8000 is invested at 12% compounded...Ch. 6 - 63. A couple borrowed $ 184,000 to buy a...Ch. 6 - Problems 64-67 are complex financial problems that...Ch. 6 - Problems 64-67 are complex financial problems that...Ch. 6 - 1. If $8000 is invested at 7% compounded...Ch. 6 - 2. Suppose you invest $100 at the end of each...Ch. 6 - 3. To buy a municipal bond that matures to $10,000...Ch. 6 - 4. A debt of $280,000 is amortized with 40 equal...Ch. 6 - 5. If an investment of $1000 grew to $ 13,500 in 9...Ch. 6 - 6. A couple borrowed $97,000 at 7.2% compounded...Ch. 6 - 7. If you borrow $2500 for 15 months at 4% simple...Ch. 6 - 8. How much must you put aside at the beginning of...Ch. 6 - 9. Find the annual percentage yield (the effective...Ch. 6 - 10. An accountant wants to withdraw $3000 from an...Ch. 6 - 11. If $10,000 is invested at 7% compounded...Ch. 6 - 12. A $780,000 IRA is used to supplement a retired...Ch. 6 - 13. What amount must you invest in an account that...Ch. 6 - 14. If $1500 is deposited at the end of each...Ch. 6 - 15. Maxine deposited $400 at the beginning of each...Ch. 6 - 16. Grandparents plan to establish a college trust...Ch. 6 - 17. A couple borrows $180,000 at 5.4% compounded...Ch. 6 - 18. Suppose that a 10-year corporate bond has a...Ch. 6 - 19. The following sequence is arithmetic: 298.8,...Ch. 6 - 20. A 400-mg dose of heart medicine is taken...Ch. 6 - 21. If you took a home mortgage loan of $150,000...Ch. 6 - 22. A couple would like to have $50,000 at the end...Ch. 6 - 23. A woman makes $3000 contributions at the end...

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