Question

Problem 6.25 (Solution Video) Crane Productions borrowed some money from the California Finance Company at a rate of 15.40 percent for a seven-year period. The loan calls for a payment of $1,340,000 each year beginning today. How much did Crane borrow? (Round factor values to 4 decimal places, e.g. 1.5214 and final answer to nearest whole dollar, e.g. 5,275) Crane borrowed Question Attempts: 0 of 2 used SAVE FOR LATER SUBMIT ANSWER

Answer 1

rate of interest = 15.40%

for 7 years

Annual payment = $1,340,000 (payment at the beginning of period - BOP)

Present value of the loan, PV:

PV = $1,340,000 + $1,340,000/(1+0.154)^1 + $1,340,000/(1+0.154)^2 + $1,340,000/(1+0.154)^3 + $1,340,000/(1+0.154)^4 + $1,340,000/(1+0.154)^5 + $1,340,000/(1+0.154)^6  

PV = $6,357,048

First Equated annual Installment (EAI) is paid at the BOP of amount $1,340,000. Second EAI is paid at the beginning of the 1st year. So its present value is $1,340,000/(1+0.154)^1. Similarly other installments till the last installment paid at the beginning of the 6th year, whose PV = $1,340,000/(1+0.154)^6.

Below is the amortization table for the same (with payments at the BOP)

Year	Beg Loan o/s	EAI	Interest Paid	Principal Paid	End o/s
0	$6,357,048	$1,340,000	0	$1,340,000	$5,017,048
1	$5,017,048	$1,340,000	$772,625.33	$567,375	$4,449,673
2	$4,449,673	$1,340,000	$685,249.63	$654,750	$3,794,923
3	$3,794,923	$1,340,000	$584,418.07	$755,582	$3,039,341
4	$3,039,341	$1,340,000	$468,058.45	$871,942	$2,167,399
5	$2,167,399	$1,340,000	$333,779.45	$1,006,221	$1,161,179
6	$1,161,179	$1,340,000	$178,821.49	$1,161,179	($0)
		$9,380,000		$6,357,048

Loan borrowed: $6,357,048

Answer: 6,357,000 (nearest to whole dollar)