Question

The manager of Gloria's Boutique has approved Carla's application for 24 months of credit with maximum monthly payments of $70. If the APR is 14.2 percent, what is the maximum initial purchase that Carla can buy on credit?A) $1,006.90B) $1,300.00C) $1,455.08D) $1,184.75E) $1,228.46

Answer 1

To find Carla's maximum initial credit purchase, present value of her $70 monthly payments for 24 months with a 14.2% APR was calculated, yielding approximately $1,006.90. This is option A.

Step-by-step explanation:

To calculate the maximum initial purchase Carla can buy on credit, we first need to understand that this is a problem related to the calculation of the present value of an annuity. In this case, the annuity is the series of $70 monthly payments that Carla is able to make. Using the formula for the present value of an annuity, we have PV = PMT * [(1 - (1 + r)^-n)/r], where PMT is the monthly payment amount, r is the monthly interest rate, and n is the number of payments.

First, we convert the APR to a monthly interest rate by dividing by 12 (months). This gives us 14.2% / 12 = 1.1833% per month, or 0.011833 as a decimal. Carla's number of payments is 24 (for 24 months).

The formula now becomes:
PV = 70 * [(1 - (1 + 0.011833)⁻²⁴) / 0.011833]

Calculating this, we find the present value (PV), which is the maximum initial purchase Carla can afford on credit. After solving the formula, we find that the closest answer to the computed PV is $1,006.90, which corresponds to option A.

Answer 2

C) $1,455.08

Step-by-step explanation:

Formula = M = [P (1 + r)^n * r] / [(1 + r)^n - 1]

Putting the figures in the formula =

$70 = P [(1 + 0.142/12)^24 * 0.142/12 ] / [(1 + 0.142/12)^24 - 1]

=> $70 = P (1.326209535) * 0.142/12 / 0.326209535

=> $70 = P * 0.0156934795 / 0.326209535

=> P = $1455.08

So, the maximum initial purchase that Carla can buy on credit = $1455.08