Intermediate Accounting: Reporting And Analysis
Intermediate Accounting: Reporting And Analysis
3rd Edition
ISBN: 9781337788281
Author: James M. Wahlen, Jefferson P. Jones, Donald Pagach
Publisher: Cengage Learning
Question
Book Icon
Chapter M, Problem 9P

1.

To determine

Determine the required number of deposit and the amount of last deposit.

1.

Expert Solution
Check Mark

Explanation of Solution

 Annuity: An annuity is referred as a sequence of payment of fixed amount of cash flows that occurs over the equal intervals of time.

Cash flow occurs during the first day of each time period is known as an annuity due, whereas cash flow occurs during the last day of each time period is known as an ordinary annuity.

FVO represents Future Value of ordinary annuity = $40,000, and i represents interest rate for each of the stated time periods = 7% (14%2) per semi-annum

Determine the number of deposits required.

FVO=Cash flow ×(fon,i)$40,000=$4,000 ×(fon=?,i=7%)$40,000$4,000=(fon=?,i=7%)10.000000=(fon=?,i=7%)

In the future value of an ordinary annuity of $1 table (at the end of the time value money module), it can be identified that the factor of 10.000000 is lies between 7 and 8 number of period at 7% column. This reveals that T Houser has to make 7 deposits of $4,000 each, and the 8th deposit would be less than the amount of $4,000.

Now, to determine the amount of the last deposit, first calculate the future value of an annuity due of 7 deposits of $4,000 at 7%, using future value of annuity due formula.

FVD=cash flow ×(fDn=7,i=7%)FVD=cash flow ×(fOn+1=8,i=7%1)FVD=$4,000 ×(10.2598031)FVD=$4,000 ×9.259803

FVD=$37,039.21

Here,

FVD represents future value of annuity due.

Here, 10.259803 is taken from Future value of ordinary annuity of $1 table, where n = 8, i =7%. Factor of annuity due is calculated with the help of ordinary annuity table, as there is no separate table provided in this module for future value of annuity due.

Finally, determine the amount of required last deposit.

Amount of last deposit = [Fund need to accumulateFuture valueof annuity due of 7 deposits]=$40,000$37,039.21=$2,960.79

Therefore, the amount of last deposit will be $2,960.79.

Conclusion

Therefore, the required number of deposit of $4,000 each 6 months is 7 and the amount of last deposit is $2,960.79.

2.

To determine

Determine the required number of payments need to be made and the amount of last payment.

2.

Expert Solution
Check Mark

Explanation of Solution

 Annuity: An annuity is referred as a sequence of payment of fixed amount of cash flows that occurs over the equal intervals of time.

Cash flow occurs during the first day of each time period is known as an annuity due, whereas cash flow occurs during the last day of each time period is known as an ordinary annuity.

PVO represents Present Value of ordinary annuity = $20,000.

Determine the number of payments required.

PVO=Cash flow ×(pon,i)$20,000=$4,000 ×(pon=?,i=12%)$20,000$4,000=(pon=?,i=12%)5.000000=(pon=?,i=12%)

In the present value of an ordinary annuity of $1 table (at the end of the time value money module), it can be identified that the factor of 5.000000 is lies between 8 and 9 number of period at 12% column. This reveals that Person JC has to make 8 payments of $4,000 each year, and the 9th payment would be less than the amount of $4,000.

Now, determine the amount of reduction in principal after 8th payment, using present value of ordinary annuity formula (PVO).

PVO=Cash flow ×(pOn=8,i=12%)PVO=$4,000×4.967640PVO=$19,870.56

Here, 4.967640 is taken from Present value of ordinary annuity of $1 table, where n = 8, i =12%.

Now, $129.44 ($20,000$19,870.56) of the original principal is yet to be paid by Person JC. This $124.44 will accrue interest at 12% interest rate in 9th year.

Now, determine the amount of required last payment.

FV =PV×(fn,i)FV =$129.44×(fn=9,i=12%)FV =$129.44×2.773079FV = $358.95

Hence, the amount of last payment will be $358.95.

This 2.773079 is taken from Future value of $1 table, where n = 9, i =12%.

Conclusion

Determine the required number of payment of $4,000 each year is 8 and the amount of last payment is $358.95.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!
Students have asked these similar questions
What's the depreciation?
Answer
Prepare journal entries to below Question

Chapter M Solutions

Intermediate Accounting: Reporting And Analysis

Ch. M - Prob. 11GICh. M - Prob. 12GICh. M - Prob. 13GICh. M - Prob. 14GICh. M - Prob. 15GICh. M - Prob. 16GICh. M - Prob. 17GICh. M - Prob. 18GICh. M - Prob. 19GICh. M - Prob. 20GICh. M - Prob. 21GICh. M - Prob. 22GICh. M - What is a deferred ordinary annuity? How does it...Ch. M - Prob. 24GICh. M - Prob. 25GICh. M - Give two examples of assets and three examples of...Ch. M - Prob. 1MCCh. M - Prob. 2MCCh. M - Refer to the present value table information on...Ch. M - Refer to the present value table information on...Ch. M - On May 1, 2019, a company purchased a new machine...Ch. M - An office equipment representative has a machine...Ch. M - Prob. 7MCCh. M - For which of the following transactions would the...Ch. M - On July 1, 2019, James Rago signed an agreement to...Ch. M - On January 1, 2019, Ken Company sold a machine to...Ch. M - Prob. 1RECh. M - Based on the following annual interest rates, what...Ch. M - Prob. 3RECh. M - Prob. 4RECh. M - Next Level Potter wishes to deposit a sum that at...Ch. M - Prob. 6RECh. M - Prob. 7RECh. M - Prob. 8RECh. M - Prob. 9RECh. M - If 90,000 is invested in a fund on December 31,...Ch. M - Samuel Ames owes 20,000 to a friend. He wants to...Ch. M - Prob. 12RECh. M - Prob. 13RECh. M - Prob. 14RECh. M - Prob. 1ECh. M - Future Value Hugh Colson deposited 20,000 in a...Ch. M - Prob. 3ECh. M - Future Value of Annuity Using appropriate tables,...Ch. M - Prob. 5ECh. M - Prob. 6ECh. M - Prob. 7ECh. M - Cash Flow Amounts R. Lee Rouse borrows 10,000 that...Ch. M - Prob. 9ECh. M - Amount of an Annuity John Goodheart wishes to...Ch. M - Prob. 11ECh. M - Prob. 12ECh. M - Present Value of Leased Asset On January 1, 2019,...Ch. M - Amount of an Annuity Beginning December 31, 2023,...Ch. M - Prob. 1PCh. M - Prob. 2PCh. M - Prob. 3PCh. M - Determining Loan Repayments Jerry Rockness needs...Ch. M - Prob. 5PCh. M - Prob. 6PCh. M - Value of an Annuity Using the appropriate tables,...Ch. M - Serial Installments; Amounts Applicable to...Ch. M - Prob. 9PCh. M - Comprehensive Part a. Reproduced in the following...Ch. M - Prob. 11PCh. M - Present Value of an Annuity John Joshua wants to...Ch. M - Present Value of an Annuity Ralph Benke wants to...Ch. M - Compound Interest Issues You are given the...Ch. M - Cash Flow Amounts On January 1, 2019, Philip...Ch. M - Prob. 16PCh. M - Comprehensive The following are three independent...Ch. M - Prob. 18PCh. M - Asset Purchase Price BWP Inc. is considering the...Ch. M - Prob. 1CCh. M - Prob. 2CCh. M - Prob. 3CCh. M - Prob. 4CCh. M - Prob. 5C
Knowledge Booster
Background pattern image
Recommended textbooks for you
Text book image
Intermediate Accounting: Reporting And Analysis
Accounting
ISBN:9781337788281
Author:James M. Wahlen, Jefferson P. Jones, Donald Pagach
Publisher:Cengage Learning
Text book image
Excel Applications for Accounting Principles
Accounting
ISBN:9781111581565
Author:Gaylord N. Smith
Publisher:Cengage Learning