If you can invest $1,000 today and it will grow to be worth $1,350 over the next 6 years, what is the compound annual return you will earn on this investment?
Business · High School · Tue Nov 03 2020
Answered on
Given:
Principal Amount (P) = $1000
Future Amount (A) =$1350
Term (t) = 6 years
Compounded annually(n) = 1
Determine the annual return or the rate of the investment.
Formula for compound interest.
A = P ( 1 + r/n)^nt
Solution:
Substitute the given values to the formula for compound interest.
$1350 = $1000 ( 1 + r/1)^(6)(1)
$1350 = $1000 ( 1 + r)^6
$1350 = $1000 ( 1 + r^6)
$1350 /$1000=( 1 + r^6)
1.35 = 1 + r^6
350 =1000r^6
Divide both sides by 1000.
350/1000 = r^6
Take the sixth root of both sides in order to cancel out r^6. Taking the sixth root is the same as raising the number by 1/6
(0.35)^1/6 = (r^6)^1/6
r = 0.84 or 84%
Final answer:
r = 0.84 or 84%