If you deposit $2000 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) = 2000(1 + r)3, where r is written as a decimal.. . . what interest rate will yield a balance of $2300 after 3 years? . . . a. . 4.55%. . c. . 4.67% . . b. . 3.25% . d. . 4.77% .

The future worth of the ) current investment with compounded interest is given by the equation,
                                      B(c) = P(1 + r)^3
From the given above,
                                      B(c) = 2000(1 + r)^3
The rate may be obtained by rearranging the equation,
                                       (1 + r)^3 = B(c) / 2000
                                  ((1 + r)^3)^1/3 = (B (c) / 2000) ^1/3
                                         r = (2300 / 2000)^1/3 - 1
The value of r is 0.477. Thus, the answer is letter D..