55.The manager of Bonzai's Boutique has approved Carla's application for credit. The maximum payment that has been approved is $95 a month for 24 months. The APR is 16 percent. What is the maximum initial purchase that Carla can make given this credit approval

$1,916.2

Explanation:

A fix Payment for a specified period of time is called annuity. The discounting of these payment on a specified rate is known as present value of annuity. In this question the payment of $95 per month for 24 months at APR of 16% is an annuity.

Formula for Present value of annuity is as follow

PV of annuity = P x [ ( 1- ( 1+ r )^-n ) / r ]

Where P = Annual payment = $95

First, Calculate the effective rate

EAR = ( 1 + 16%/12 )^12 - 1 = 17.2%

r = rate of return = 17.2% annual = 17.2% / 12 = 1.44% per month

n = number of years = 24 months

Placing value in the Formula

PV of annuity = $95 x [ ( 1- ( 1+ 1.44% )^-24 ) / 1.44% ]

PV of Annuity = $1,916.2

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