formul.t: of compound interest. 117 



A rental ;• is due at the end of each year, altogether n 

 times ; its value at the end of ii years is — 



'Op 



b. Prexent V'due. 



A rental R becomes due for the first time after m years, 

 and is payable altogether n times after intervals of in. years ; 

 its present value is — 



^ ij a-or^-D 



l-Ojf" il-Op'" - 1) ^ ^ 



A rental r is due at the end of ea -h year, altogether n 

 times ; its present value is — 



^ r (l-0^>» - 1) 



1-Oy' X -Op ■ • • ^vi.; 



A rental r is due at the end of each year, for ever ; its 

 present value is — 



<'o=TJr- ■ ■ ■ (VII.) 



•Op 



A rental B is due after ii years, and again every n years, 

 for ever^ its present value is — 



'•■ = roi?^i • • •(^™-> 



A rental It is due after m years, and again every n years, 

 for ever ; its present value is — 



1-Op'^ - 1 ^ ^ 



A rental It is due now, and again after every n years, for 

 ever ; its present value is — 



_ It X ro/v- 

 ^" - l-0/>" - 1 • • • ^^'^ 



