math
posted by Jackie on .
a) 1150 dollars invested at 9% annual interest rate (compounded yearly) or
b) 1475 invested at 6% annual interest (compounded yearly) after
When would the two investments have equal value?

let the time be t
1150(1.09)^t = 1475(1.06)^t
46(1.09)^t = 59(1.06)^t
take log of both sides , and using simple log rules
log46 + tlog1.09 = log59 + tlog1.06
tlog1.09  tlog1.06 = log 59  lot 46
t(log 1.09  log 1.06) = log 59  log 46
t = (log59 log46)/(log1.09  log1.06) = 8.918
it would take appr 9 years
check:
1150(1.09^9 = 2497.68
1475(1.06)9 = 2491.98
using t = 8.918
1150(1.09)^8.918 = 2480.09
1475(1.06)^8.918 = 2480.13 , not bad