The interest is supposed compound unless the contrary is state.If 25 years' purchase must be paid for an annuity to continue n years, and 30 years' purchase for an annuity to continue 2n years, find the rate per cent.
Given: 25 years and 30 years are the present values of the annuity for n,2n years respectively.
Let r be the rate of interest.
The, 25=1−r−nr−1...(i)
and 30=1−r−2nr−1...(ii)
Divide (ii) by (i), we get
3025=1−r−2n1−r−n
⇒65=(1−r−n)(1+r−n)1−r−n
⇒65=1+r−n
⇒r−n=65−1
⇒1rn=15
⇒r=51n%