Question

You are taking out an $11,000 loan today at 7% compounded annually. You will pay back the loan with 6 equal end-of-year payments.

How much interest will you owe in the third year?

How much will you owe the bank at the end of the third year?

Show necessary formulas to find equal payment, principal payment, and interest payments.

Answer 1

Amount borrowed = $11,000
Interest rate = 7%
Period = 6 years

Let annual payment be $x

$11,000 = $x / 1.07 + $x / 1.07^2 + ... + $x / 1.07^6
$11,000 = $x * (1 - (1/1.07)^6) / 0.07
$11,000 = $x * 4.766540
$x = $2,307.75

Annual payment = $2,307.75

Year 1:

Beginning loan outstanding = $11,000

Interest Paid = 7% * Beginning loan outstanding
Interest Paid = 7% * $11,000
Interest Paid = $770

Principal paid = Annual payment - Interest Paid
Principal paid = $2,307.75 - $770.00
Principal paid = $1,537.75

Ending loan outstanding = Beginning loan outstanding - Principal paid
Ending loan outstanding = $11,000 - $1,537.75
Ending loan outstanding = $9,462.25

Year 2:

Beginning loan outstanding = $9,462.25

Interest Paid = 7% * Beginning loan outstanding
Interest Paid = 7% * $9,462.25
Interest Paid = $662.36

Principal paid = Annual payment - Interest Paid
Principal paid = $2,307.75 - $662.36
Principal paid = $1,645.39

Ending loan outstanding = Beginning loan outstanding - Principal paid
Ending loan outstanding = $9,462.25 - $1,645.39
Ending loan outstanding = $7,816.86

Year 3:

Beginning loan outstanding = $7,816.86

Interest Paid = 7% * Beginning loan outstanding
Interest Paid = 7% * $7,816.86
Interest Paid = $547.18

Principal paid = Annual payment - Interest Paid
Principal paid = $2,307.75 - $547.18
Principal paid = $1,760.57

Ending loan outstanding = Beginning loan outstanding - Principal paid
Ending loan outstanding = $7,816.86 - $1,760.57
Ending loan outstanding = $6,056.29

Interest owed in third year is $547.18 and amount owed to bank at the end of third year is $6,056.29