Respuesta :
Answer:
The money will last for approximately 10 years.
Explanation:
Assuming the withdrawal to spend $2,100 is made at the end of each year, the relevant formula to use is therefore the formula for calculating the present value (PV) of an ordinary annuity as follows:
PV = P * [{1 - [1 / (1 + r)]^n} / r] …………………………………. (1)
Where;
PV = Present value of the inheritance left by your great aunt = $15,000
P = yearly withdrawal = $2,100
r = interest rate = 6.5%, or 0.065
n = number of years the money will last = ?
Substitute the values into equation (1) and solve for n as follows:
15,000 = 2,100 * [{1 - [1 / (1 + 0.065)]^n} / 0.065]
15,000 / 2,100 = {1 - [1 / 1.065]^n} / 0.065
7.14285714285714 = [1 - 0.938967136150235^n] / 0.065
7.14285714285714 * 0.065 = 1 - 0.938967136150235^n
0.464285714285714 = 1 - 0.938967136150235^n
0.938967136150235^n = 1 - 0.464285714285714
0.938967136150235^n = 0.535714285714286
Loglinearize both sides, we have:
n * log 0.938967136150235 = log 0.535714285714286
n = log 0.535714285714286 / log 0.938967136150235
n = -0.271066772286538 / -0.0273496077747564
n = 9.9112 years, or approximately 10 years
Therefore, the money will last for approximately 10 years.
