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!
