Question

For an investment to double in value during a 12-year period,

a. What annually compounded rate of return must it earn? (Round your answer to two decimal places.)

Annually compounded rate of return %

b. What monthly compounded rate of return must it earn? (Round your answer to two decimal places.)

Answer 1

a. P = Po(1+r)^12 = 2Po
Divide both sides by Po:
(1+r)^12 = 2
Take Log of both sides:
12*Log(1+r) = Log 2
Divide both sides by 12:
Log(1+r) = Log 2/12 = 0.02509
1+r = 10^(0.02509) = 1.0595
r = 0.0595 = 5.95%

b. 12Comp./yr. * 12yrs. = 144 Compounding periods.

P = Po(1+r)^144 = 2Po
r = Monthly % rate expressed as a decimal.
Solve for r.
Use same procedure as part a.