Carl purchased a $242 car stereo at Worst Buy. He paid $28 at the time of purchase and agreed to pay the balance in 12 equal monthly payments. The finance charge was 14% simple interest. What was the amount of each payment?
$Theactualpriceofthecarstudio=\$242.\phantom{\rule{0ex}{0ex}}Butsince,\$28hasalreadybeenpaid,theinitialvalue(ortheprincipalamount)willbe:\$242-\$28=\$214.\phantom{\rule{0ex}{0ex}}Also,wearegiven:\phantom{\rule{0ex}{0ex}}Rate\left(r\right)=14\%\phantom{\rule{0ex}{0ex}}Time\left(t\right)=12months=1year.$
$Therefore,thetotalamountthatneedstobepaidisgivenbytheformula:\phantom{\rule{0ex}{0ex}}A=P(1+rt)\phantom{\rule{0ex}{0ex}}A=214(1+(0.14).1)\phantom{\rule{0ex}{0ex}}A=214(1+(0.14\left)\right)\phantom{\rule{0ex}{0ex}}A=214(1.14)\phantom{\rule{0ex}{0ex}}A=243.96\phantom{\rule{0ex}{0ex}}Nowwegetthatthetotalpayableamount,thatistheprincipalamount+alltheinterestis\$353.8.\phantom{\rule{0ex}{0ex}}Nowthisamountneedstobepaidin12equalpayments.\phantom{\rule{0ex}{0ex}}Therefore,theamountthatneedstopaidineachinstallmentis:\phantom{\rule{0ex}{0ex}}\{243.96\}/\left\{12\right\}=20.33\phantom{\rule{0ex}{0ex}}So,eachmonthCarlneedstopay\$20.33$