The cash flow diagram of Option-2 is shown again for ready reference.

Fig. 2.8 Cash flow diagram of Option-2 with annual income split into uniform base amount and gradient amount (shown for ready reference)

The equivalent present worth of the gradient series (of the annual income) starting from end of year ‘4' will be located at the end of year ‘2'. The future worth of this amount at end of year ‘10' will be obtained by multiplying the equivalent present worth ‘ P_g ' (shown in Fig. 2.8) at the end of year ‘2' with the single payment compound amount factor (F/P, i, n) . The equivalent future worth (in Rs.) of Option-2 is determined as follows;

Now replacing P_g with G (P/G, i, n) i.e. 5000( P/G, 8%, 8 ) in the above expression;

It may be noted here that, in the above expression, 5000 (P/G, 8%, 8) (F/P, 8%, 8) can be replaced by 5000 (F/G, 8%, 8) and will result in the same value.

Now putting the values of different compound interest factors in the above expression;

FW₂= - 6476700 + 1738392 + 164787 + 800000

FW₂ = - Rs.3773521