Question

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?

Answer 1

r = ∛(B/1000) -1

Explanation:

Solve for r by undoing the math operations that are done to it, in reverse order. The operations done to r are ...

• add 1
• raise the sum to the 3rd power
• multiply by 1000

To undo these operations, we start from the bottom of the list and work up.

B = 1000(1 +r)^3

B/1000 = (1 +r)^3 . . . . undo the multiplication: divide by 1000

∛(B/1000) = 1 +r . . . . raise both sides to the 1/3 power to eliminate the exponent of 3

∛(B/1000) -1 = r . . . . . subtract 1 to undo the addition of 1

The interest rate required to achieve a balance of B in 3 years is given by the formula ...

r = ∛(B/1000) -1