Math Word Problem

Question

What annual compound interest rate is required for a $18837 investment to grow into $36286 in 12 years if interest is compounded monthly?

Round your answer to the nearest tenth of a percent. 

Answer 1

the underlying compound interest formula that you want to use to solve this one is

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

for this set of values that becomes

36286 = 18837(1 + r/12)^(12*12)

solving that for "r" using technology i end up getting

r = 0.0548 x 100% = 5.48%

meaning that the annual compound interest rate required here is 5.48%

Answer 2

36286 = 18837 *(1+r/12)^144

1.92631523.... (1 + r/12)^144

log(1.92631523....)/144 = log(1 + r/12)

10^((log(1.92631523....)/144 ))= 1+ r/12

12[(10^(log(1.92631523....)/144 ))-1 ] = r

= 0.0547585477803.......... or just over 5.475%