how many years will it take an investment of 1000 to double if the interest rate is 6% compounded annually

11.9 years

Step-by-step explanation:

The compound amount formula applicable here is A = P (1+r) ^t.

Substituting the given data, $2000 = $1000 (1.06) ^t, or 2 = 1.06^t.

Taking the log of both sides, log 2 = t log 1.06. Then t = 0.30103/0.02531, or t = 11.896.

The investment will doube in 11.9 years.

Years = {log (total) - log (Principal) } : log (1 + rate)

Years = log (2,000) - log (1,000) / log (1.06)

Years = 3.3010299957 - 3 / 0.025305865265

Years =.3010299957 / 0.025305865265

Years = 11.8956610473 or about 11.9 Years