Amortization Problem

[tfs985]

I am doing a chapter on Loans and Amortization and I have an issue with this problem:

A man buys a car for $36,000. If the interest rate on the loan is 12%, compounded monthly, and if he wants to make monthly payments of $900 for 36 months, how much must he put down.

The answer in the back of the book is $8,903.25.

The only formulas my teacher has taught me has been the amortization formula and the formula for how to calculate the unpaid balance. I have no idea where to even begin on this problem! Any help would be appreciated.

 

[TchrWill]

I am doing a chapter on Loans and Amortization and I have an issue with this problem:

A man buys a car for $36,000. If the interest rate on the loan is 12%, compounded monthly, and if he wants to make monthly payments of $900 for 36 months, how much must he put down.

The answer in the back of the book is $8,903.25.

The only formulas my teacher has taught me has been the amortization formula and the formula for how to calculate the unpaid balance. I have no idea where to even begin on this problem! Any help would be appreciated.

The formula for calculating a monthly loan payment is R = Pi/[1 - 1/(1+i)^n] where R = the periodic payment, P = the principal, or debt to be paid off, n = the number of payment periods over which the payments will take place, and i = the periodic interest rate in decimal form. The interest rate for a loan is usually quoted as an annual rate such as 8%. In the formula the first thing we do is convert this to i = .08 when considering annual payments. If payments are to be made monthly, i = .08/12 = .006666 as the monthly interest rate. An example will illustrate the use of the formula.

You have R, n and i. Solve for P and subtract from $36,000.

 

[JeffM]

I am doing a chapter on Loans and Amortization and I have an issue with this problem:

A man buys a car for $36,000. If the interest rate on the loan is 12%, compounded monthly, and if he wants to make monthly payments of $900 for 36 months, how much must he put down.

The answer in the back of the book is $8,903.25.

The only formulas my teacher has taught me has been the amortization formula and the formula for how to calculate the unpaid balance. I have no idea where to even begin on this problem! Any help would be appreciated.

The amortization formulas etc are derived from the present value computation of an annuity. Were you taught how to calclulate the present value of an annuity?

If so, calclulate the present value of 36 monthly payments at 12% per year compounded monthly. That tells you what those future payments are worth today, right now.

So the person selling the car wants 36,000 now, right? And the future payments are worth what NOW? So how much must you pay now for the seller to receive $36,000 in value now?

Basically all this amortization stuff comes down to present value or future value computations.

 

[tfs985]

I am doing a chapter on Loans and Amortization and I have an issue with this problem:

A man buys a car for $36,000. If the interest rate on the loan is 12%, compounded monthly, and if he wants to make monthly payments of $900 for 36 months, how much must he put down.

The answer in the back of the book is $8,903.25.

The only formulas my teacher has taught me has been the amortization formula and the formula for how to calculate the unpaid balance. I have no idea where to even begin on this problem! Any help would be appreciated.

The amortization formulas etc are derived from the present value computation of an annuity. Were you taught how to calclulate the present value of an annuity?

If so, calclulate the present value of 36 monthly payments at 12% per year compounded monthly. That tells you what those future payments are worth today, right now.

So the person selling the car wants 36,000 now, right? And the future payments are worth what NOW? So how much must you pay now for the seller to receive $36,000 in value now?

Basically all this amortization stuff comes down to present value or future value computations.

The present value of an annuity is in my book, so I will go through all the steps you listed and let you know what I come up with. I have class now so I'm gonna try and figure this thing out later tonight when I get back. Thanks for the help, I appreciate it.

 

[JeffM]

Good luck.

You can always come back after you have done more work and show us where you are stuck.

By the way, Tchrwill made a very important point. When payments are made at periods different from yearly but the interest rate is quoted as an annual rate, you must ADJUST the rate approrpiately. If i = the annual rate and the number of payments per year is r, the interest rate to use in the formulas is i / r.