need help with basic annuities question.

[sm9764]

Here is the question:

A loan of $12,000 is to be repaid within one yr. with level monthly payments, due at the beginning of of each month.

The 12 payments equal $1000 each.
A finance charge of $632 is also due with the first payment.

Calculate the effective annual interest rate of the loan?

here's what I come up with:

12000 = (1000 + 632) + 1000 (a'') 11 | i

the equation they have is: (correct one)

12000 = (1000+632) + 1000 a 11 | i

they are saying in the problem that the payment is due at the beginning of each month, therefore it suppose to be annunity-Due, but somehow they are using annuity immediate.

Any idea why, please explain.

Thanks!

[Arnold Kim]

Here is the question:

A loan of $12,000 is to be repaid within one yr. with level monthly payments, due at the beginning of of each month.

The 12 payments equal $1000 each.
A finance charge of $632 is also due with the first payment.

Calculate the effective annual interest rate of the loan?

here's what I come up with:

12000 = (1000 + 632) + 1000 (a'') 11 | i

the equation they have is: (correct one)

12000 = (1000+632) + 1000 a 11 | i

they are saying in the problem that the payment is due at the beginning of each month, therefore it suppose to be annunity-Due, but somehow they are using annuity immediate.

Any idea why, please explain.

Thanks!

Because you already have the first payment, which is $1,632. All subsequent payments begin coming once a month, starting one month later, which means that their present value would then be calculated like an annuity-immediate.

If you wanted to use the annuity due formula, the formula should look like:

12000 = 632 + 1000 (a'') 12| i

[sm9764]

Yes, it makes perfect sense now. but somehow the answer does not match with the book answer.

Ans: 12.7%

any idea?:confused:

[Arnold Kim]

Yes, it makes perfect sense now. but somehow the answer does not match with the book answer.

Ans: 12.7%

any idea?:confused:

I mistakenly put i in the denominator when it should have been d. That might be the problem

[Arnold Kim]

Oh, and what you might be getting is the monthly interest rate- I forgot to convert that to effective annual the first time I tried it. Monthly interest is0.999386%, which converted annually is 12.674%.

[sm9764]

yep! that's it... I tried to convert it by using effective rate interest formula, got some off value. Can you post the method you used.

Thanks!

[Arnold Kim]

I just did 1.00999386^12.

[sm9764]

Yeah, I forgot dividing .999386/100. Thanks man..

[Ken]

You guys should really be using your calculator. It makes life much easier.
PV = -(12000-632)
2nd beginning of year payments
pmt = 1000
n = 12
12P/Y
1 C/Y
and you get i = 12.674%.