Sums of digits method - Example - PLEASE HELP

Hi guys,

I have seen a few examples of the sum of digits method to calculate interest on a lease. However, I cannot understand how the below has been calculated?

“A company leases plant on 1st Jan 20X4 worth £9,000 for 4 years. They pay 4 instalments of £3,000 beginning on the 31st Dec 20X4. What is the interest charge at 31st Dec 20X5?” ANSWDER: £900

My calculation was as follows:
- 4 instalments of £3,000 = £12,000 due. (Which means £12,000 due - £9,000 worth = £3,000 interest total payable)
- Total digits is 10
n(n+1)/2
4(4+1)/2
- I figure that the 31st Dec 20X5 is the second year, which means there are 2 remaining useful years.
- Interest X (Remaining years/Digits)
£3,000 X (2/10) = £600 Interest – WRONG

I know I am doing something completely obvious that is wrong but I CANNOT understand what. Please could someone point the obvious out to me? In the answer they have done: £3,000 X (3/10) = £900.... But why have they used 3??


Thanks so much,