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I have a debt of $1000 and have the option of paying it upfront or pay in 12 equal interest-free instalments.

Can someone calculate the Future Value difference between the 2, assuming banks are giving me interest rate at 3.0% APY?

It definitely makes more sense to pay in instalments since it's interest-free, but I want to know how much difference there is at the end of 12 months. Is it just the added interest component of $13+ or is it more appropriate that I need to double that since there's inflation?

Not sure why I keep thinking that the appropriate amount should be double that.

cashflow calculation

hs123
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    sometimes with these types of deals there is a penalty if you miss a payment, so that any savings will disappear if you miss it by one day. – mhoran_psprep Jan 06 '24 at 13:10
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    Your calculations are wrong. You need to calculate future value of $1000 as well. That would be $1000 + 30% = $1030. The correct cash flow difference of future values of the two will be $16.13. – Utkarsh Jan 06 '24 at 18:13
  • Depending on the terms of the deal, the risk is if you miss a payment, you get charged ALL of the back interest, usually as significantly higher rates. So only do it if you are ABSOLUTELY SURE you can make each payment on time. – D Stanley Jan 10 '24 at 16:26

2 Answers2

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Assuming the debt is due to $1000 in the bank, from which a repayment p can be taken at the end of each month for 12 months.

p = 1000/12

Calculating the balance at the end of the first month a[1], based on $1000, s, at monthly rate r (from the APY effective rate), less repayment p.

s = 1000
r = (1 + 0.03)^(1/12) - 1
a[1] = s (1 + r) - p

Balances at the end of the second and third months are

a[2] = a[1] (1 + r) - p
a[3] = a[2] (1 + r) - p

In general a[n] = (p + (1 + r)^n (r s - p))/r

a[12] = 16.3234

$16.32 would be gained by making the monthly repayments compared to repaying the $1000 debt from the bank immediately, for no gain or loss.

The same via Excel

=FV((1 + 0.03)^(1/12) - 1, 12, 1000/12, -1000)
Chris Degnen
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You are making it a lot complicated. And you missed to calculate the future value of $1000.

The easiest way to do this job is to simply use Excel to calculate future value of given cash flows. There is an in-built function for calculating future value.

To calculate FV of 12 monthly instalments of $83.333 at 3% rate per annum or 0.25% per month, use the following formula:
= FV(0.25%, 12, 83.333)

This will return -1,013.86, with negative sign denoting cash outflow.

Now to calculate FV of lumpsum money of $1000 at 3% rate per annum, use the same formula:
=FV(3%, 1, 1000, , 1).

This will return -1,030.00.

You should opt for first choice as it involves less cash outflow of $16.13.

Utkarsh
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