Math Problem Help

Question

What annual compound interest rate is required for a $11865 investment to grow into $38155 in 12 years if interest is compounded monthly?

Round your answer to the nearest tenth of a percent. 

Answer 1

A(t) = P(1+r/n)^(nt)

A(t) = amount in t years

P = initial investment (principal)

r = annual interest rate

n = number of compoundings per year

So, 38155 = 11865(1+r/12)^[(12)(12)]

3.21576 = (1+r/12)^144

log(3.21576) = 144log(1+r/12)

log(1+r/12) = 0.0035228

1+r/12 = 10^(0.0035228)

1+r/12 = 1.0081445

r/12 = 0.0081445 So, r = 9.8%