Question

A borrower had a loan of $30,000.00 at 5% compounded annually, with 7 annual payments. Suppose the borrower paid off the loan after 4 years. Calculate the amount needed to pay off the loan. The amount needed to pay off this loan after 4 years is $ (Round to the nearest cent as needed.)

Answer 1

Answer: 14,118.91

Calculations:

Installment paid at the end of the each year = Borrowed amount ÷ Present value annuity factor (5%, 7 years)

Installment paid at the end of the each year = $30,000/5.78637

Installment paid at the end of the each year = $5,184.60

Interest amortization table
Year	Cash paid	Interest expense	Decrease in Carrying value	Carrying value
0				$       30,000.00
1	$ 5,184.60	$            1,500.00	$                                   3,684.60	$       26,315.40
2	$ 5,184.60	$            1,315.77	$                                   3,868.83	$       22,446.57
3	$ 5,184.60	$            1,122.33	$                                   4,062.27	$       18,384.30
4	$ 5,184.60	$                919.21	$                                   4,265.39	$       14,118.91
5	$ 5,184.60	$                705.95	$                                   4,478.65	$         9,640.26
6	$ 5,184.60	$                482.01	$                                   4,702.59	$         4,937.67
7	$ 5,184.60	$                246.88	$                                   4,937.72	$                      -

Interest expense = Preceding carrying value x 5%

Decrease in carrying value = Cash paid - Interest expense

Carrying value = Preceding carrying value - Interest expense

Carrying value after 4 payments is $14,118.91.

Hence, Amount need to pay off the loan after 4 payments is $14,118.91