Given;
#"Rate" rArr r = 4.5%#
#"Principal" rArr p = p#
#"Compund" rArr n = 1/4# (quarterly #=3/12#)
#"Compund Interest" rArr A = 2p# (if the amount of d money doubles)
#"No of years" rArr t = ?yrs#
Hence we solve;
#A = p(1+r/n)^(nt)#
Inputing the values above;
#2p = p(1 + 4.5 xx 4)^(1/4 xx t)#
#2p = p(1 + 18)^(t/4)#
#2p = p(19)^(t/4)#
Divide both sides by #p#
#(2p)/p = (p(19)^(t/4))/p#
#(2cancelp)/cancelp = (cancelp(19)^(t/4))/cancelp#
#2 = 19^(t/4)#
Multiply both sides by the power of #4/t#..
#2^(4/t) = 19^(t/4 xx 4/t)#
#2^(4/t) =19#
Take #log# of both sides..
#log 2^(4/t) = log 19#
#4/tlog2 = log19#
Divide both sides by #log2#
#(4/tlog2)/log2 = log19/log2#
#(4/tcancellog2)/cancellog2 = log19/log2#
#4/t = log19/log2#
#4/t = 4.248#
Cross multiplying..
#4/t = 4.248/1#
#4 xx 1 = 4.248 xx t#
#4 = 4.248t#
Divide both sides by #4.248#
#4/4.248 = (4.248t)/4.248#
#4/4.248 = (cancel4.248t)/cancel4.248#
#4/4.248 = t#
#t = 0.94yrs -> "to the nearest tenth as required"#
Hope this helps!
