Question

4. On 1/1/87, Cathy borrows $1,000 from ABS Finance Company and agrees to pay it back in five annual installments at an annual effective rate of 11%. The first payment is due one year after the loan is issued. On 1/1/89 Cathy pays off the balance of the loan plus a $50 prepayment penalty. Find ABC's effective overall yield rate i. Select one: a. 12.8% <i< 13.0% O b. 13.4% <i O c. 13.0% <i< 13.2% d. 13.2% < i < 13.4% O e. i < 12.8%

Answer 1

CATHY'S BORROWING AMOUNT = 1000 $

BORROWING DATE = 01/01/1987

TENNUE = 5 YEARS

INTEREST RATE = 11%

IF WE CALCULATE EQUAL ANNUAL INSTALLMENT FROM ABOVE INFORMATION IT COMES TO 260.88$ PER YEAR. IN FOLLOWING I AM SHOWING YOU THE REPAYMENT TABLE.

Year	Principal	Interest	Total Paid	Balance
1987	$158.71	$102.17	$260.88	$841.29
1988	$177.10	$83.78	$260.88	$664.19
1989	$197.58	$63.30	$260.88	$466.61
1990	$220.45	$40.43	$260.88	$246.16
1991	$246.16	$14.94	$261.10	$0.00
Totals	$1,000.00	$304.62	$1,304.62

NOW CATHY REPAID THE BALANCE AMOUNT ON 01/01/1989.

SO CATHY MADE FULL PAYMENT OF FIRST TWO YEAR.

01/01/1987 TO 31/12/1987 = FIRST INSTALLMENT = 158.71 + 102.17 = 260.88

01/01/ 1988 TO 31/12/1988 = SECOND INSTALLMENT = 177.10 + 83.78 = 260.88

NOW 01/01/19989 CATHY PAID BALANCE AMOUNT IN FULL. SO REMAINING BALANCE IS 1000 - 158.71-177.10 = 664.19

NOW TOTAL INTEREST RECEIVED FROM BOTH INSTALLMETS TO ABC CO. IS = 102.17 + 83.78 = 185.95

NOW ABC FINANCE COMPANY RECEIVES EXTRA 50$ FOR PREPAYAMENT OF LOAN.

SO TOTAL EXTRA RECEIVED BY ABC FINANCE CO IS = 185.95 + 50 = 235.95$

SO FOR 1000 LOAN GIVEN TO CATHY, ABC FINANCE RECEIVES 235.95$.

SO HERE, EFFECTIVE RATE WILL BE = (235.95 / 1000) * 100 = 23.60%

SO HERE THE ANSWER WILL BE INTEREST (i) MORE THAN OR EQUAL TO 13.4%