PV ordinary general annuity

[bitesnbites]

after completing this problem and related ones in a practice exercise, i am always some few cents off according to the answer key, can someone please help me see what im doing in error?

A bakery was purchased for $40,000 down + $25,000 payments at the end of every 6 months for the next 5 years. The interest rate is 18% compound monthly, what was the cash price? Answer key: $198,038.15

What I come up with: $198,038.59

 

[Deleted member 4993]

after completing this problem and related ones in a practice exercise, i am always some few cents off according to the answer key, can someone please help me see what im doing in error?

A bakery was purchased for $40,000 down + $25,000 payments at the end of every 6 months for the next 5 years. The interest rate is 18% compound monthly, what was the cash price? Answer key: $198,038.15

What I come up with: $198,038.59

View attachment 3186View attachment 3187View attachment 3188View attachment 3185

These are all round-off error:

A = 25000*(1.59070403)/0.09344326 = 25000 * 6.3215611

I got these result using MS_Excel.

If you are looking for accuracy of the order of ~10^-8 ( to the penny, where the numbers are in ~10⁶ dollars) - you'll need to do the intermediate calculations with ~10 digits. Regular scientific calculators do the calculations with 8 digits - thus the discrepancy.

 

[bitesnbites]

Makes me "nervous" to see how you use the "formula".

Start by handling the rate conversion:
(1 + i)^2 = (1 + .18/12)^12 ; solve:
i = (1 + .18/12)^6 - 1 ; comes out to: .09344326....

Now calculate the Present Value:
PV = 25000[1 - 1/(1+i)^10] / i ; comes out to: 158038.1528739....

...and tell your teacher it's kinda silly to include the $40,000 down payment
in this problem, as it's got nothing to do with the "actual" calculation

Actually i'm using the same method & steps as provided by their material as weird as that looks. They provide their "own" book to offer a different perspective in addition to the actual text book. Used their methods all the way with no problems, one unit away now having issues. I have math skills of a 6th grader, but need this one course. Sort of noticing "their" methods are quite different from the average formulas. Thanks for the explanation.

These are all round-off error:

A = 25000*(1.59070403)/0.09344326 = 25000 * 6.3215611

I got these result using MS_Excel.

If you are looking for accuracy of the order of ~10^-8 ( to the penny, where the numbers are in ~10⁶ dollars) - you'll need to do the intermediate calculations with ~10 digits. Regular scientific calculators do the calculations with 8 digits - thus the discrepancy.

Kind of noticed this when i tried another calculator

Thanks, i'm sure ill be back again when I get stuck.