How to derive the A(n-1) formula? I have got the answers but I do not understand the logic of the problem. Please explain. Thanks.

5. At the end of year 5, an investment has grown to $750. This investment has earned annual effective rates of interest equal to i, = 0.007511-0.0015 since issue. What was the size of the initial investment made at time 0? ALO) =K in :0.00755 -0.0015 = A(n)-A(n-) A(n-1) Aln-DAco) (Itin) A14- 750 1+(0-0375 -0.0015) 750 = $723.9382239 1.0366 A13) 223.93227239 - $703.8177092 A(2): 7703.8779092 1.0210 = $ 689.4003028 AC)-_689.400308 1-0135 = $680.2173684 ACC), 680.2123684 1.0060 $676-1604059 = 9676.16 1.0285