Statistics. If this medal costs to ` , every year and the rate of compound interest is %, then what amount is to be deposited now. Here a = , and i = . P = i .
= , = , . Therefore the amount to be deposited is ` , . Example . A limited company wants to create a fund to help their employees in critical circumstances.
The estimated expenses per month is ` , . Find the amount to be deposited by the company if the rate of compound interest is %. Here a = , ; i = . and k = .
P = i k , . = , , Therefore the amount to be deposited is ` , , . Example . Find the annual rate of interest, to get a perpetuity of ` for every half yearly from the present value of ` , .
Solution : Here P = , ; a = ; k = , i = ? P = a i k , = ⇒ i = = = . Rate of interest ( i )= . × % = .
% Exercise . . Find the amount of an ordinary annuity of ` , per annum for years at the rate of interest of % per year. [( .
) = . ]. . If the payment of ` , is made at the end of every quarter for years at the rate of % per year, then find the amount of annuity.
Find the amount of an ordinary annuity of monthly payments of ` , that earns interest at % per annum compounded monthly. [( . ) = . ].
- - Financial Mathematics . A bank pays % per annum interest compounded quarterly. Find the equal deposits to be made at the end of each quarter for years to have ` , ? [( .
) = . ]. . A person deposits ` ,