If you deposit $1000 in a savings account with an interest rate of r compounded annually?
If you deposit $1000 in a savings account with an interest rate of r compounded annually, then the balance in the account after 3 years is given by the function B(c)=1000(1+r)^3, where r is written as a decimal.
What is the formula for the interest rate, r; required to achieve a balance of B in the account after 3 years?
- llafferLv 71 year agoFavorite Answer
You are given the equation:
B = 1000(1 + r)³
And asked to solve for r in terms of B. So let's start with dividing 1000 from both sides:
B / 1000 = (1 + r)³
Now we can get the cube root of both sides:
∛(B / 1000) = 1 + r
And finally, subtract 1 from both sides:
r = ∛(B / 1000) - 1
Since 1000 = 10³, we can simplify that to be:
r = ∛(B / 10³) - 1
r = ∛(B) / 10 - 1
This matches option B of your choices.