If the exact question was “which is the better offer?” then the pay monthly option is not necessarily a wrong answer, they have only misunderstood if it was more explicitly “which has the lower interest rate?”.

]]>If you borrowed the money at 20% with monthly payments, the payment would be $92.63 per month.

So what would you rather pay — $100 a month or $92.63 per month?

The higher amount is 20% compounded annually. The lower amount is 20% annual rate compounded monthly.

The difference is not the total amount paid but the rate and the number of payments per year. ]]>

Even though I understand the principle I was more looking at it from Nils’ point of view, “where is the benefit” and it appears from a reply I got back from Tim, that the benefit is you can then use the money saved to pay off other debt.

This is of course moot, if like me, you have no debt, don’t run a CC balance, and don’t buy in instalments, but hey ho…

]]>You can calculate the net present value by discounting each installment by 1,66% (that’s 20% interest divided by 12 months); that would be 100/1.0166+100/1.0166^2+…100/1.66^12. This gives a value of £1079,51, which represents the actual price of the computer if you were to buy it now.

Note this is almost £80,- higher! So you’re actually coughing up an additional £80 today to pay in monthly installments.

The implicit interest rate of almost 30% is found when we add the interest rate (20%) of the other option: 1079,51*1,2=1295,41, that is 29,51%

This can be attributed to the time value of money: an amount money that you have now is worth more than that same amount of money you’ll get in the future.

]]>Is it better to pay the total amount at the end of the year rather than in monthly installments because instead of forking over GBP 100 over every month, you can put it in a fixed deposit (12 months for the first GBP 100, 11 months for the second GBP 100 and so on) and thereby earn some interest from it? Is this lost interest some sort of opportunity cost when you pay in monthly installments?

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