Kim bought new furniture for $1650.00 and paid $160 as a down payment while financing the rest for 1 year at 7% interest. Find the total interest paid if she makes monthly payments.

52.66
63.84
67.76
57.10

Question

Kim bought new furniture for $1650.00 and paid $160 as a down payment while financing the rest for 1 year at 7% interest.  Find the total interest paid if she makes monthly payments.

52.66
63.84
67.76
57.10

tkhunny · Answer

How much was financed.

Note: This is a reality check question.  If you cannot answer this question correctly, you cannot be ready for the rest of the solution.  Think very carefully before answering.

anonymous · Answer

$1490 was financed total.

tkhunny · Answer

Thank you.  I hope it surprises you how many cannot get that part.  Excellent work.

Now, what's your plan for the rest of the solution?  Have you the formula for the present value of periodic payments at the end of each period?

anonymous · Answer

There are 12 payments total divided by $1490 financed but 7% is added on each month as interest?

tkhunny · Answer

I'll take that as a "no" on having the right formula?

Okay, stay with me.

We need a series of payments such some decreasing amount of interest will be charged along the way AND the entire 1490 will be paid along the way.

Let's just invent an interest factor.  I'll call it 'r'.
Let's name the level payment.  I'll call it P

Here is the goal...

After 1 month: 1490r - P
After 2 months: (1490r - P)r - P
After 3 months: ((1490r - P)r - P)r - p

Is that making sense?

anonymous · Answer

no

tkhunny · Answer

It makes sense to me.  @debi  ?

anonymous · Answer

The total interest paid would be higher than any of the possible solutions so I'm confused.

tkhunny · Answer

Amount Financed: $1,490.00

What is the Payment?  I get $128.92

Pay that 12 times.  $128.92 * 12 = $1,547.04

Interest Paid: $1,547.04 - $1,490.00 = $57.04

tkhunny · Answer

1490 * 0.07/12 = 8.69
After one month, we have 1490 + 8.69 - 128.92 = 1369.77
Total Interest Paid, so far: 8.69

1369.77 * 0.07/12 = 7.99
After two months, we have 1369.77 + 7.99 - 128.92 = 1248.84
Total Interest Paid, so far: 8.69 + 7.99 = 16.68

1248.84 * 0.07/12 = 7.28
After three months, we have 1248.84 + 7.28 - 128.92 = 1127.20
Total Interest Paid, so far: 16.68 + 7.28 = 23.96

anonymous · Answer

I'll work on it this way...I was using the compound interest formula = annuity formula.

tkhunny · Answer

Right, that's where the payment amount comes from.  I keep trying to show folks how to make their own, but so far, no one seems to want to know.  I thought you might be the first.