If $6,000 is invested at 6% per year compounded monthly, the future value S at any time t (in months) is given by S = 6,000(1.005)t.

Question

What is the amount after one year?

How long before the investment doubles?

Answer 1

Your equation is not quite correct. FV = 6000(!+i/12)^twe have to compound.. we want FV/PV = 2 so 2 = ((1.05)^t so we take natural logs of b oth sides ant get t*ln(1.05)=ln(2) ln (2) = .6931. and ln(1.005)=138.97 months or 11.58 years.. After 1 year, 6000 will be worth 6000*(1.005)¹²

=6,370.07