Question

Zebina purchased an entertainment center for $2,798 using a 12-month deferred payment plan with an interest rate of 21.95%. She did not make any payments during the deferment period. What will the total cost of the entertainment center be if she must pay it off within six years after the deferment period?

$5,236.80

$6,284.16

$2,798.00

$3,477.88

Answer 1

no payments are made during the deferment period, but interest is still added on during this time, so

A = P(1+r/n)^(n*t)


A = 2798(1+0.2195/12)^(12*1)


A = 3477.87513984319


A = 3477.88


This means that after the 12 month deferment period is up, the balance will be 3477.88 dollars

--------------------------------------

now turn to the formula

T = (c*L*n)/(1 - (1+c)^(-n))

where

T = total loan cost
c = monthly interest rate (c = r/12)
L = loan principal amount (basically the initial balance you need to pay off)
n = number of payment periods (ie number of months)

In this case:

T = unknown (solving for this)
L = 3477.88
c = 0.0182916666666667 (c = r/12 = 0.2195/12 = 0.0182916666666667)
n = 72 (ie number of months)


plug all that in to get

Loan Total Cost = (c*L*n)/(1 - (1+c)^(-n))


Loan Total Cost = (0.0182916666666667*3477.88*72)/(1 - (1+0.0182916666666667)^(-72))


Loan Total Cost = 6284.33759299891


Loan Total Cost = 6284.34


So this is pretty close to $6,284.16, which is choice B, but I'm not 100% sure why there is this much roundoff error