Total purchase cost

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serena

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Mar 17, 2023
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So, I've been doing online exercises of command annual interest, but I'm having a lot of trouble with this one, the other exercises are ok. I tried everything, but the system always says it's not the right answer. Our teacher did not taught us this at all and is not going to help us.

Exercise:
An advance payment of 16.79% will be given upon purchase. The rest will be paid after 48 months taking into account a compound annual interest rate of 5.57%. The advance payment is €525.95. How much will the purchase ultimately cost (accurate to 2 decimal places)?

I thought it was like this:
€525.95 / 16.79% = 3.132,52
K = P x (1 + i)^n
K = (83,21% x 3.132,52) x (1 + 5,57%)^48/12
K = 3237,66

Total purchase cost: 3237,66 + 3.132,52 = 6370,18

But it's sadly not the correct answer.
 
serena said:
So, I've been doing online exercises of command annual interest, but I'm having a lot of trouble with this one, the other exercises are ok. I tried everything, but the system always says it's not the right answer. Our teacher did not taught us this at all and is not going to help us.

Exercise:
An advance payment of 16.79% will be given upon purchase. The rest will be paid after 48 months taking into account a compound annual interest rate of 5.57%. The advance payment is €525.95. How much will the purchase ultimately cost (accurate to 2 decimal places)?

I thought it was like this:
€525.95 / 16.79% = 3.132,52
K = P x (1 + i)^n
K = (83,21% x 3.132,52) x (1 + 5,57%)^48/12
K = 3237,66

Total purchase cost: 3237,66 + 3.132,52 = 6370,18

But it's sadly not the correct answer.
Click to expand...
Hi @serena,

€3,237.66 is the amount you have calculated after interest has been added to the outstanding balance (after the 48 months) but €3,132.55 was the total cost before any interest was added!

All you should be adding to the €3,237.66 is the initial advance payment of €525.95 (not €3,132.52).

Does €3,237.66 + €525.95 give you the required answer?

If you had examined the difference between your calculated sum ("K = 3,237.66") and the given answer you would probably have realized your mistake. It's always worth looking at how much you are "out" by! ?
 
Last edited:
Are payments being made monthly? Or just one sum at the end of 4 years. The question, as written, reads as if the latter. Just wondering??
 
The Highlander said:
Hi @serena,

€3,237.66 is the amount you have calculated after interest has been added to the outstanding balance (after the 48 months) but €3,132.55 was the total cost before any interest was added!

All you should be adding to the €3,237.66 is the initial advance payment of €525.95 (not €3,132.52).

Does €3,237.66 + €525.95 give you the required answer?

If you had examined the difference between your calculated sum ("K = 3,237.66") and the given answer you would probably have realized your mistake. It's always worth looking at how much you are "out" by! ?
Click to expand...
Yes, it's the right answer! I mean I tried the method you suggested in the same exercise but with different numbers (it's an exercise that keeps changing but with different numbers). Thank you very much for your help!
 
serena said:
Yes, it's the right answer! I mean I tried the method you suggested in the same exercise but with different numbers (it's an exercise that keeps changing but with different numbers). Thank you very much for your help!
Click to expand...
You're very welcome (and thank you for letting us know). :)

One other suggestion, I would have liked to have made in my initial response but it only occurred to me afterwards:-

I always advise students to approach problems like this in smaller, discrete stages rather than trying to construct "comprehensive" expressions (like your "K = (83,21% x 3.132,52) x (1 + 5,57%)^48/12") as working through problems that way aids understanding and facilitates checking of results as you go along.

For example (in this case) I might write down:-

1. Advance payment: €525.95 is 16.79% of total ⇒ Total (initial) cost is €3,132.52 (525.95 ÷ 0.1679)

2. Total (initial) Cost: €3,132.52, less the €525.95 paid "up front" ⇒ a balance of €2,606.57 (3132.52 - 525.95) will be subject to interest at 5.57% p.a. over 4 years (48 months)

3. Outstanding Balance: 2606.57 × 1.0557⁴ = 3237.66 (initial balance plus interest) ⇒ final balance of €3,237.66 is due to be paid after 48 months.

4. Total cost is, therefore, Advance Payment plus outstanding Balance (plus interest), ie: €525.95 + €3,237.66 which comes to an ultimate total cost for the purchase of €3,763.61.

Doing it that way (or in a similar fashion that suits you) in small(er) steps will keep you 'focused' on what each result arrived at 'means' and enable you to quickly spot any errors in your thought processes.

Hope that helps. ?

Kind Regards.
 
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