Question

A loan 1000 is repaid by equal annual amounts of principal for 10 years and annual interest of 7% on the outstanding balance.

Answer 1

Answer:

This payment is an annuity, because the payments are of equal amount, periodic, and under the same interest rate. Thus, to find the answer, we use the present value of an annuity formula:

P = A [(1-(1+i)^-n) / i]

Where:

P = Present value of the loan

A = Value of the annuity (the value we will find)

i = interest rate

n = number of periods

We plug the amounts into the formula:

1,000 = A [(1-(1+0.07)^-10) / 0.07]

1,000 = A [7.02358]

1,000 / 7.02358 = A

142.4 = A

So the periodic payment is $142.4 per year, for 10 years, meaning that they payment schedule would be:

Year     Payment     Principal    Interest   Balance

1            $142.4        $100           $42.4     $900

2           $142.4        $100           $42.4     $800

3           $142.4        $100           $42.4     $700

4           $142.4        $100           $42.4     $600

5           $142.4        $100           $42.4     $500

6           $142.4        $100           $42.4     $400

7           $142.4        $100           $42.4     $300

8           $142.4        $100           $42.4     $200

9           $142.4        $100           $42.4     $100

10          $142.4       $100           $42.4        $0