1.
Determine the accumulated amount in the savings account on December 31, 2021.
1.
Answer to Problem 11E
The accumulated amount in the savings account on December 31, 2021 is $64,041.28.
Explanation of Solution
Future Value: The future value is value of present amount compounded at an interest rate until a particular future date.
Person HD deposits $40,000 on January 1, 2016. Interest rate of 8% is compounded semiannually. Thus the interest rate per one half-year is 4%
Determine the future value as on January 1, 2016.
Hence, the amount of $40,000 deposited for 12 semi annum at 4% interest compounded semi-annually will have a future value of $64,041.28.
Note:
FV stands for Future value
PV stands for Present value
i stands for interest rate for each of the stated time periods
n stands for number of time periods
FV factor (Future value of $1: n = 12, i =4%) is taken from the table value (Table 1 at the end of the time value money module).
2.
Determine the accumulated amount in the fund on December 31, 2020, after the receipt of December 31 bonuses of 2020.
2.
Answer to Problem 11E
Accumulated amount in the fund on December 31, 2020, after the receipt of December 31 bonuses of 2020 is $31,764.24.
Explanation of Solution
Person BJ deposits the bonus amount of $5,000 each year in his savings accounts, starts from December 31, 2016. Deposit will earn 12% interest per annum. Number of time period from December 31, 2016 to December 31, 2020 is 5 years.
Determine the future value ordinary annuity.
Hence, the amount of $5,000 deposited each year for 5 years at 12% compound interest has a future value of $31,764.24.
Note:
FVO stands for future value ordinary annuity
i stands for interest rate for each of the stated time periods
n stands for number of time periods
fO stands for factor of annuity due
Future value of ordinary annuity of $1: n =5, i =12% is taken from the table value (Table 2 at the end of the time value money module).
3.
Determine the amount to be paid on January 1, 2019 by Person RS.
3.
Answer to Problem 11E
The amount to be paid on January 1, 2016 by Person RS is $11,566.29.
Explanation of Solution
Person RS owes $30,000 on a non- interest bearing note due January 1, 2026. On January 1, 2016 he offers to pay the amount after discounting the note at 10% compounded annually.
Determine the present value as on January 1, 2016.
Hence, Person RS would have to pay $11,566.29, on January 1, 2016.
Note:
FV stands for Future value
PV stands for Present value
i stands for interest rate for each of the stated time periods
n stands for number of time periods
PV factor (Present value of $1: n = 10, i =10%) is taken from the table value (Table 3 at the end of the time value money module).
4.
Determine the cost of annuity for Person JS.
4.
Answer to Problem 11E
The cost of annuity for Person JS is $50,303.06.
Explanation of Solution
Person JS will receive $6,000 each period on June 30 and December 31 for the next 6 years, from the annuity purchased on January 1, 2016. Interest rate is 12% per annum.
Number of time period from June 30, 2016 to December 31, 2022 is 12 semi annum.
Determine the present value ordinary annuity (Cost of annuity).
Hence, the cost of annuity is $50,303.06.
Note:
PVO stands for present value ordinary annuity
i stands for interest rate for each of the stated time periods
n stands for number of time periods
PO stands for factor of present value ordinary annuity
Present value of ordinary annuity of $1: n =12, i =6% is taken from the table value (Table 4 at the end of the time value money module).
5.
Determine the amount of equal annual contribution.
5.
Answer to Problem 11E
Amount of equal annual contribution would be $4,467.20.
Explanation of Solution
n – 5 annual cash flows
I – Interest rate 10% compounded annually
Future value – $30,000
First cash flow starts on December 31, 2016, and December 31, 2020 is the last cash flow. Here, the cash flow occurs during the first day of each time period, hence it is an annuity due.
Determine the future value annuity due.
Hence, the 5 equal annual contributions are $4,467.20.
Note:
Future ValueD stands for future value annuity due
Future value of ordinary annuity of $1: n = 6, i =10% is taken from the table value (Table 2 at the end of the time value money module).
There is no separate table provided in this module for future value of annuity due. Thus, factor of annuity due is calculated with the help of ordinary annuity table.
6.
Determine the amount of equal annual withdrawals.
6.
Answer to Problem 11E
Amount of equal annual withdrawals would be $2,525.68.
Explanation of Solution
n – 6 equal future annual withdrawals start from December 31, 2027.
I –Interest rate 10% compounded annually
Investment (Present value) – $11,000
Here, the cash flow occurs during the last day of each time period, hence it is an ordinary annuity.
Determine the present value ordinary annuity.
Hence, the 6 equal annual withdrawals would be $2,525.68.
Note:
Present value of ordinary annuity of $1: n = 6, i =10% is taken from the table value (Table 4 at the end of the time value money module).
Want to see more full solutions like this?
Chapter M Solutions
Intermediate Accounting: Reporting and Analysis
- Samuel Ames owes 20,000 to a friend. He wants to know how much he would have to pay if he paid the debt in 3 annual installments at the end of each year, which would include interest at 14%. Draw a time line for the problem. Indicate what table to use. Look up the table value and place it in a brief formula. Solve.arrow_forwardDetermining Loan Repayments Jerry Rockness needs 40,000 to pay off a loan due on December 31, 2028. His plans included the making of 10 annual deposits beginning on December 31, 2019, in accumulating a fund to pay off the loan. Without making a precise calculation, Jerry made 3 annual deposits of 4,000 each on December 31, 2019, 2020, and 2021, which have been earning interest at 10% compounded annually. Required: What is the equal amount of each of the next 7 deposits for the period December 31, 2022, to December 31, 2028, to reach the fund objective, assuming that the fund will continue to earn interest at 10% compounded annually?arrow_forwardAmount of an Annuity John Goodheart wishes to provide for 6 annual withdrawals of 3,000 each beginning January 1, 2029. He wishes to make 10 annual deposits beginning January 1, 2019, with the last deposit to be made on January 1, 2028. Required: If the fund earns interest compounded annually at 10%, how much is each of the 10 deposits?arrow_forward
- Refer to the present value table information on the previous page. What amount should Brett have in his bank account today, before withdrawal, if he needs 2,000 each year for 4 years, with the first withdrawal to be made today and each subsequent withdrawal at 1-year intervals? (Brett is to have exactly a zero balance in his bank account after the fourth withdrawal.) a. 2,000 + (2,000 0.926) + (2,000 0. 857) + (2,000 0.794) b. 2,0000.7354 c. (2,000 0.926) + (2,000 0.857) + (2,000 0.794) + (2,000 0.735) d. 2,0000.9264arrow_forwardOn January 1, 2021, you deposited $5,500 in a savings account. The account will earn 10 percent annual compound interest, which will be added to the fund balance at the end of each year. Required: 1. What will be the balance in the savings account at the end of 9 years? (Future Value of $1.Present Value of $1. Future Value Annuity of $1. Present Value Annuity of $1.) Note: Use appropriate factor(s) from the tables provided.arrow_forwardMrs. Quiton deposited Php 120,000.00 into a college fund at the beginning of every month for 10 years . The fund earns 9% annual interest , compounded monthly . She paid at the end of the month . How much is in the account right after the last deposit ? 1. What is the type of annuity illustrated in the given problem? A. Simple Annuity B. General Annuity C. Deferred Annuity D. Complex Annuity 2. Determine the present value of the deposit. A. Php 12,000.00 B. Php 30,000.00 C. Php 60,000.00 D. Php 75,000.00arrow_forward
- Cynthia wants to accumulate at least $40,000 by depositing $1,200 at the end of each month into a fund that earns interest at 5.75% compounded monthly. a. How many deposits does she need to make in order to reach her goal? Round to the next payment b. How long will it take Cynthia to reach her goal? year(s) month(s) Express the answer in years and months, rounded to the next payment periodarrow_forwardQuestion: On May 1, 2020, Hazel borrowed a sum of money from Far East Bank , payable for 2 years at 8% simple interest. She paid P6,000 for the interest of her loan. Find how much was borrowed by Hazel.arrow_forward13. Walrus opens up a savings account on January 1 2024, and here are the series of his transactions over the next two years. Withdrawal Deposit Date 01/01/2024 60000 04/01/2024 07/01/2024 10/01/2024 07/01/2025 30000 10/01/2025 10000 15000 20000 106 48. Find i. 5000 The fund accumulates according to simple interest with an annual effective interest rate of i. By December 31 2025, the fund has accumulated to 41242.arrow_forward
- Ricky Fowler borrowed $70,000 on March 1, 2018. This amount plus accrued interest at 6% compounded semiannually is to be repaid March 1, 2028. To retire this debt, Ricky plans to contribute to a debt retirement fund five equal amounts starting on March 1, 2023, and for the next 4 years. The fund is expected to earn 5% per annum. Instructions How much must be contributed each year by Ricky Fowler to provide a fund sufficient to retire the debt on March 1, 2028?arrow_forwardUsing the appropriate interest table, provide the solution to each of the following four questions by computing the unknowns. a. What is the amount of the payments that Ned Winslow must make at the end of each of 8 years to accumulate a fund of $90,000 by the end of the eighth year, if the fund earns 8% interest, compounded annually? b. Robert Hitchcock is 40 years old today and he wishes to accumulate $500,000 by his sixty-fifth birthday so he can retire to his summer place on Lake Hopatcong. He wishes to accumulate this amount by making equal deposits on his fortieth through his sixty-fourth birthdays. What annual deposit must Robert make if the fund will earn 8% interest compounded annually? c. Diane Ross has $20,000 to invest today at 9% to pay a debt of $47,347. How many years will it take her to accumulate enough to liquidate the debt? d. Cindy Houston has a $27,600 debt that she wishes to repay 4 years from today; she has $19,553 that she intends to invest for the 4…arrow_forwardi) Identify whether Simple or General Annuity ii) Identify whether Ordinary Annuity, Annuity Due, or Deferred Annuity iii) Using the formula, solve for the unknown iv) Use tabular presentation to support your answer 4) Clyde is setting up a fund of $12,000 fund to purchase a brand new cellphone. If he deposits $800 in a bank every end of the month which pays an interest of 9% compounded monthly, how long will it take him to raise the desired amount?arrow_forward
- Intermediate Accounting: Reporting And AnalysisAccountingISBN:9781337788281Author:James M. Wahlen, Jefferson P. Jones, Donald PagachPublisher:Cengage LearningExcel Applications for Accounting PrinciplesAccountingISBN:9781111581565Author:Gaylord N. SmithPublisher:Cengage Learning