MATH SOLVE

6 months ago

Q:
# Jackson purchased some power tools totaling $1,543 using a six month deferred payment plan with an interest rate of 23.76%. He did not make any payments during the deferment period. What will the total cost of the power tools set be if he must pay off the power tools within two years after the deferment period?$1,543.00 $1,735.63 $2,197.44 $2,746.80

Accepted Solution

A:

Suppose he makes the payment with two equal annual instalments, the present value of the amount he is owing is $1,543 , the interest rate is 23.76% = 0.2376.

The amount of payment he makes in two of the periodic payments is given by:

[tex]PV = P\left( \frac{1-(1+r)^{-n}}{r} \right) \\ \\ \Rightarrow1,543=P\left( \frac{1-(1+0.2376)^{-2}}{0.2376} \right) \\ \\ =P\left( \frac{1-(1.2376)^{-2}}{0.2376} \right)=P\left( \frac{1-0.6529}{0.2376} \right) \\ \\ =P\left( \frac{0.3471}{0.2376} \right)=1.4609P \\ \\ \Rightarrow P= \frac{1,543}{1.4609} =1,056.20[/tex]

Therefore, in 2 years, the amount he has paid for the tools is 2(1,056.20) = 2,112.40

The amount of payment he makes in two of the periodic payments is given by:

[tex]PV = P\left( \frac{1-(1+r)^{-n}}{r} \right) \\ \\ \Rightarrow1,543=P\left( \frac{1-(1+0.2376)^{-2}}{0.2376} \right) \\ \\ =P\left( \frac{1-(1.2376)^{-2}}{0.2376} \right)=P\left( \frac{1-0.6529}{0.2376} \right) \\ \\ =P\left( \frac{0.3471}{0.2376} \right)=1.4609P \\ \\ \Rightarrow P= \frac{1,543}{1.4609} =1,056.20[/tex]

Therefore, in 2 years, the amount he has paid for the tools is 2(1,056.20) = 2,112.40