Interest formula

Question

What interest rate to the nearest percent is needed to grow 5,000 to 8,000 in 5 years if interest is compounded annually?

Answer 1

8000=5000(1+r)^6

Then we solve for r

1.08=1+r

r=0.08

Answer 2

Use the Compound Interest Formula to solve for the interest rate:

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

Where

A = The final amount

P = The initial amount

r = Rate

n = number of times compounded per year

t = time in years

Just fill in the formula with the known values and solve for the unknown value(r):

8000 = 5000(1+r/1)^1*5

Divide r by 1 and Multiply 5 by 1:

8000 = 5000(1+r)⁵

Divide both sides of the equation by 5000:

1.6 = (1+r)⁵

Get rid of the exponent by taking the fifth root of both sides of the equation:

1.0985 = 1+r

Subtract 1 from both sides of the equation:

0.0985 = r

Now multiply r by 100 to turn the rate from a decimal to a percent:

r = 9.85%

The Correct Answer is: 9.85%