Answer:
The correct option is a. $15,198.
Explanation:
This can be calculated using the formula for calculating the present value of an ordinary annuity as follows:
PV = P * ((1 - (1 / (1 + r))^n) / r) …………………………………. (1)
Where;
PV = Present value of the loan or the largest loan amount that can be gotten =?
P = Monthly payment = $350
r = Monthly interest rate = APR / 12 = 5% / 12 = 0.05 / 12 = 0.00416666666666667
n = number of months = 4 years * 12 months = 48
Substitute the values into equation (1) to have:
PV = $350 * ((1 - (1 / (1 + 0.00416666666666667))^48) / 0.00416666666666667)
PV = $350 * 43.4229559379367
PV = $15,198.0345782779
Rounding to a whole dollar amount, we have:
PV = $15,198
Therefore, the correct option is a. $15,198.
The largest amount of a loan we can get at an APR of 5% is: a. $15,198.
Using this formula
PV = P ×((1 - (1 / (1 + r))^n) / r)
Where:
PV =Present value=?
Principal= $350
r = Interest rate=0.05 / 12 = 0.004167
n = 4 years × 12 = 48
Let plug in the formula
PV = $350× [(1 - (1 / (1 + 0.004167))^48)]/ 0.004167
PV = $350× [(1 - (1 / (1.004167))^48)]/ 0.004167
PV = $350× [(1 - (1 / (1.004167)^48)]/ 0.004167
PV= $350× (1 -0.8190579663)/ 0.004167
PV= $350× (0.180942034/0.004167)
PV= $350× 43.4226144
PV=$15,197.9
PV=$15,198 (Approximately)
Inconclusion the largest amount of a loan we can get at an APR of 5% is: a. $15,198.
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