What interest rate would be necessary for $1,450 investment to grow to $5,000 in an account compounded monthly for 6 years? % (enter your answer as a percentage rounded to two decimal places)

Question

What interest rate would be necessary for $1,450 investment to grow to $5,000 in an account compounded monthly for 6 years?

 

%

 (enter your answer as a percentage rounded to two decimal places)

 

Answer 1

5000=1450(1+r/12)^12(6)

500/145 = (1+r/12)^72

1+r/12 = the 72nd root of 100/29

r/12 = -1 + 1.017= .017

r = 12(.017)= .2081

r = about 20.81% interest rate

compounded monthly to yield $5000

with investment of $1450

in 6 years

as a rough check

compare the interest rate needed

i compounded continuously

5000=1450e^6r

100/29 = e^6r

6r = ln(100/29)

r = ln(100/29)/6

r = 20.63%

which is slightly less than 20.81%

due to more compounding