Question

1

Answer 1

How much is paid?

Answer 2

Doesn't give say how much is paid. That's what has me confused.

Answer 3

Do you have an accumulation formula for periodic payments at the end of each period? We can build one if you don't.

Answer 4

No formula.

Answer 5

Well, that makes it a bit more difficult.

Let's try this. What would the payment be if there were only one payment?

Answer 6

260,000 but there should be 216 payments on 18 years.

Answer 7

Don't get ahead of your self. This is the tricky part.

What would the payment be if there were TWO payments, one month apart?

Answer 8

130000?

Answer 9

Not quite. You didn't pay any interest.

First Payment is P
First Payment increased by interest is Pr, where r is an interest factor.
Second Payment is P
Total is Pr + P = 260000
Since we know r -- Wait!! Do we know r?

Answer 10

r=.045

Answer 11

Good call, but not quite.

4.5% is the annual interest rate. We need a monthly interest accumulation factor.

I = 0.045 -- Annual Interest Rate
j = I/12 = 0.00375 -- Monthly Interest Rate
r = (1+j) = 1.00375 -- Monthly Accumulation Factor

Now we know r!!

Pr + P = 260000
P(r+1) = 260000
P = 260000/(r+1) = 129756.71

It's just a little less than 130,000.

Do you see all of this, so far? We're almost at the end.

Answer 12

yes....

Answer 13

Now the fun question.

What if there are 216 payments? What is the level payment?

Answer 14

600.73? or am I way off?

Answer 15

Where did you get that? Show your work. Use that 2-payment idea!

Answer 16

129756.71/216 = 600.7255093

Answer 17

No good. You keep forgetting to pay interest.

If it were 3 payments, it would look like this

\(Pr^{2} + Pr + P = 260000\)
\(P(r^{2} + r + 1) = 260000\)
\(P = 260000/(r^{2} + r + 1)\)

If it were 4 payments, it would look like this

\(Pr^{3 + }Pr^{2} + Pr + P = 260000\)
\(P(r^{3} + r^{2} + r + 1) = 260000\)
\(P = 260000/(r^{3} + r^{2} + r + 1)\)

Seem reasonable?