Chapter M, Problem 9P

### Intermediate Accounting: Reporting...

3rd Edition
James M. Wahlen + 2 others
ISBN: 9781337788281

Chapter
Section

### Intermediate Accounting: Reporting...

3rd Edition
James M. Wahlen + 2 others
ISBN: 9781337788281
Textbook Problem
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# Number of Cash Flows The following are two independent situations.Required: 1. Ted Houser wishes to accumulate a fund of $40,000 for the purchase of a house and lot. He plans to deposit$4,000 semiannually at the end of each 6 months. Assuming interest at 14% a year compounded semiannually, bow many deposits of $4,000 each will be required, and what is the amount of the last deposit? 2. On January 1,2019, Joan Campbell borrows$20,000 from Susan Rone and agrees to repay this amount in payments of $4,000 a year until the debt is paid in full. Payments are to be of an equal amount and are to include interest at 12% on the unpaid balance of principal at the beginning of each period. Assuming that the first payment is to be nude on January 1, 2020, determine the number of payments of$4,000 each to be nude and the amount of the final payment. Using the appropriate tablet, solve each of the preceding situations.

1.

To determine

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

Explanation

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

2.

To determine

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

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