Amount $P is invested for n years at r%p.a compound interest. If the total amount due at the end of the n year period is $mP, then r is equal to?
2007-03-13 00:21:00 · 3 answers · asked by Whatever 1 in Science & Mathematics ➔ Mathematics
amount=p[1+r/100]^n
given it is equal to mp
mp=p[1+r/100]^n
m=[1+r/100]^n
applying logarithms
log [1+r/100]=n
m
n={log[1+r/100]}/log m
2007-03-13 01:00:46 · answer #1 · answered by satwik 2 · 0⤊ 0⤋
Amount due after 1 year = P * (1+r/100) = P + Pr/100
2 year = (P+Pr/100)*(1+r/100) = P+Pr/100+Pr/100+Pr^2/10000=
=P*(1+2r/100+r^2/10000)= P*(1+2r/100+(r/100)^2))
3 year = P*(1+2r/100+(r/100)^2)*(1+r/100)=
=P*(1+2r/100+(r/100)^2+r/100+2(r/100)^2+(r/100)^3)=
=P*(1+3r/100+3(r/100)^2+(r/100)^3)
In other words:
m = (1+r/100)^n
2007-03-13 00:40:48 · answer #2 · answered by blighmaster 3 · 0⤊ 0⤋
log(1+r) = (logmP - logP)/n is the answer.
2007-03-13 00:40:42 · answer #3 · answered by bach 2 · 0⤊ 0⤋