P PiF PiX

The second method gives the same result as the first, allowing a small margin for the effects of rounding.!

It is worth noting here that although it is natural to think about the symbol P as meaning a cash flow at time 0, the present, and F as meaning a cash flow in the future, in fact these symbols can be more general in meaning. As illustrated in the last example, we can consider any point in time to be the "present" for calculation purposes, and similarly any point in time to be the "future," provided P is some point in time earlier than F. This observation gives us substantial flexibility in analyzing cash flows.

EXAMPLE 3.4

Clarence bought a flat for £94 000 in 2002. He made a £14 000 down payment and negotiated a mortgage from the previous owner for the balance. Clarence agreed to pay the previous owner £2000 per month at 12% nominal interest, compounded monthly. How long did it take him to pay back the mortgage?

Clarence borrowed only £80 000, since he made a £14 000 down payment. The £2000 payments form an annuity over Nmonths where ./Vis unknown. The interest rate per month is 1 %. We must find the value of N such that

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