Answer:
It would take Bernadette approximately <u>33 months</u> to completely pay off the stereo system.
Explanation:
Since it is assumed that Bernadette makes her payment when she sees her statement at the end of each month, we use the formula for calculating the present value (PV) of an ordinary annuity to determine the number of months as follows:
PV = M * ((1 - (1 / (1 + r))^n) / r) …………………………………. (1)
Where;
PV = Present value of the new stereo system = $400
M = minimum monthly payment = $15
r = monthly interest rate = 15% / 12 = 0.15 / 12 = 0.0125
n = number of months = n
Substitute the values into equation (1) and solve for n as follows:
400 = 15 * ((1 - (1 / (1 + 0.0125))^n) / 0.0125)
400 / 15 = (1 - (1 / 1.0125)^n) / 0.0125
26.6666666666667 * 0.0125 = 1 - (1 / 1.0125)^n
0.333333333333334 = 1 - 0.987654320987654^n
0.987654320987654^n = 1 - 0.333333333333334
0.987654320987654^n = 0.666666666666666
Loglinearizing both sides, we have:
n * log0.987654320987654 = log0.666666666666666
n * (-0.00539503188670629) = -0.176091259055682
n = -0.176091259055682 / -0.00539503188670629
n = 32.64, or 33 approximately.
Therefore, it would take Bernadette approximately <u>33 months</u> to completely pay off the stereo system.
