) – ] ⇒ a = ( . = , Therefore a = ` , Example . The age of the girl is years. Her father wants to get ` , , when his ward becomes years.
He opens an account with a bank at % rate of compound interest. What amount should he deposit at the end of every month in this recurring account? [( . ) = .
]. Here A = , , ; i = = . n = and k = A = i k a [( + k i ) nk – ] , , = ; E – ; E = a ; E = a [( . ) – ] = a [ .
– ] = a ( . ) ⇒ a = = . ∴ a ≈ , ` , is to be deposited at the end of every month. - - Financial Mathematics Example .
A person deposits ` , in the beginning of every year. If the rate of compound interest is % then ,find the amount after years . [( . ) = .
]. Solution : Here a = , ; i = . and n = . A = ( + i ) i a [( + i ) n – ] = ( + .
∴ A ≈ ` , Example . A person purchases a machine on 1st January and agrees to pay installments each of ` , at the end of every year inclusive of compound rate of %. Find the present value of the machine. [( .
) = . ]. Here n = , a = , and i = . Now