653branch leaflet, it would be displayed only during November 1999 (see Section 6 above on
654‘Bonuses’).
655
656
657
6588. Finally, consider a hypothetical product with irregular (but committed) cash flows.
659
660The pattern of this product is:
661
662 • Deposit £3,000 on 1 April in year 1, then
663 • £1,800 on 1 January each year for three years, and then
664 • £600 on 1 January in year 5,
665 • a total of £9,000 to be repaid on 1 April in year 6.
666
667
668Interest at 7% per annum is added to the account on 31 December each year and at
669repayment, together with a 2% bonus of the total amount deposited (£9,000) for making the
670required deposits and holding to maturity.
671
672Because the subsequent deposits and interest are not added on the anniversary of the first
673deposit, the AER including conditional bonuses has to be calculated on a quarterly basis and
674then compounded up to an annual rate. The calculation (in summary here, the table
675belowshows the full calculation) is as follows:
676
677First calculate the total T to be repaid at the end of the contract, using the formula:
678
679
680  20 
681 20(quarters)
682 i 
683T =  D   1+ j  
684 n
685  j=n  100  
686 n=1 
687  7  7   7 
688   3(= i3 )    4(= i7 )   (= i20 )  
689 = £3000(= D1 )  1 + 4  1 + 4  ... 1 + 4 
690  100  100   100  
691     
692     
693  7  7   7 
694   4(= i7 )    4(= i11 )   (= i20 )  
695 + £1800( = D4 )  1 + 4  1 + 4  ... 1 + 4 
696  100  100   100  
697     
698     
699 ...
700  7  7 
701   4(= i19 )   (= i20 )  
702 + £600(= D16 )  1 + 4  1 + 4 
703  100  100 
704   
705   
706 + £180 (bonusof 2% of £9,000)
707
708 = £11,785.78
709
710 13