Question

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% .

Answer 1

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..