Answer :
Benton needs to achieve an annual interest rate of approximately 6.37% to afford his purchase.
To determine the annual interest rate Benton needs to achieve in order to afford the $175,000 luxury car at the end of the 9-year period, we can use the present value of an annuity formula.
The present value of an annuity formula is:
PV = P * (1 - (1 + r)^(-n)) / r
Where:
PV = Present value of the annuity (in this case, $175,000)
P = Annuity payment per year ($15,000)
r = Annual interest rate
n = Number of years (9)
By rearranging the formula, we can solve for the interest rate (r):
r = ((P * n) - PV) / (PV * n)
Substituting the given values:
r = (($15,000 * 9) - $175,000) / ($175,000 * 9)
r ≈ 0.0637 or 6.37%
Therefore, Benton would need to achieve an annual interest rate of approximately 6.37% in order to afford the $175,000 luxury car at the end of the 9-year period.
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