I need partial help

Question

Mr. Bean wants to borrow $9200 for three years. The interest rate is 7.0% compounded monthly. I have figured out the monthly payments (857.19)

 

What will be the balance owed on the loan at the start of the third year? (Do not round intermediate calculations and round your final answer to 2 decimal places.)

Answer 1

This is a teaching moment. Your first calculation and your first help answer are both wrong. Where did you get the payment amount of $857.19? The help answer is also wrong. The equation shown in the help answer does not account for the shift in interest expense to principle reduction. The (1+ i)^n is for a single amount left on deposit that will grow to a future amount.

 

Do you have a business calculator?

Try these inputs
N= 36 (3yr * 12/mo/YR)
I= 5.8333% (7%/12)
PV = $9,200 (Loan amount)
PMT= ? (this is what we are looking for)
FV= 0 (paid off in the end)

Now hit PMT
You get $284.07

($284.07) 9200
0.07
0.005833333 Interest
Month         Beg Bal Expense Payment     Principle      End
0                9200                                    Reduction   Balance
1   $9,200.00              $53.67    $284.07  $230.40    $8,969.60
2   $8,969.60              $52.32    $284.07  $231.75     $8,737.85
3   $8,737.85              $50.97    $284.07  $233.10     $8,504.75
4   $8,504.75             $49.61    $284.07   $234.46     $8,270.29
5   $8,270.29              $48.24    $284.07  $235.83     $8,034.47
6    $8,034.47            $46.87     $284.07  $237.20      $7,797.27

32  $1,395.82             $8.14      $284.07   $275.93      $1,119.90
33  $1,119.90            $6.53      $284.07    $277.54         $842.36
34  $842.36               $4.91      $284.07    $279.16         $563.21
35  $563.21               $3.29       $284.07    $280.78        $282.42
36  $282.42               $1.65       $284.07    $282.42        $0.00


Now how much will a payment of $284.07 pay off in 12 months

Input
N=12 (one year to go)
I= 5.833% (7%/12)
PV= ? (what we are looking for)
PMT = $284.07 (has not changed)
FV= 0 (Paid Off)
Hit PV
You get $3,283.03 The new balance with 12 months to go.

Answer 2

There is an error in this problem. $9200 compounded at 7% monthly will produce a total amount of

9200 x (1 + .07/12) ^36 = $11,342.92. This should require a monthly payment of $11,342.92 / 36 = $315.08, not $857.19