Question

Juan invests 30,000 at an annual rate of 2%. How many years (approximately the closest) will be spent to double his investment if the interest is compounded monthly, then continuously ?; Compare results.

Answer 1

compounded monthly In this case p= 30000, n=12, P=2%. = 2 = 0.02 and A= 30000 X 2 = 6 mo let t years will be spend to double his invesment. Then we know A=P(1 + r ght + A =P ( 1+ 0102)27 → 60000 = 3.000 (1+ 0,02)'? =) 2 = (1 + 01002) 427 7 2 = (1.002)/27 = log2 = 127 log (1.002) → 127 = 192_ (1.002) = 347 (npromarty) =) t= 347 (Approximately, 12 = 29 year ( Approximately

Compounded continuously In This case A= pert 6.02.t = 60000 - 30000 e = 2 = e.o2t => 1og2 - (loge) (0.02) * to log 2 = 15 Y Approximate so in case of compounded monthly it will take 29 year Approximately But in the case of compounded Continvously it will take approximately 15 years so if compounded monthly it will take 14 years more than double compounded Continuously