# Sums of digits method - Example - PLEASE HELP

Pinaaa
Registered Posts:

**17**
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,

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,

## Comments

17131 Dec 20x4: £3,000 x (4/10) = £1,200

31 Dec 20x5: £3,000 x (3/10) = £900: Answer

31 Dec 20x6: £3,000 x (2/10) = £600

31 Dec 20x7: £3,000 x (1/10) = £300