Tim Worker buys a new sofa for $629.95. He pays 25% down and takes an installment loan to complete the purchase. He makes 12 payments which include his principal and a $60.00 finance charge. What is the APR on his loan to the nearest tenth? The down payment is? The amount financed is? The monthly payment will be? At the end of one year the monthly payments will total? The finance charge for one year ÷ amount financed is?
downpayment = 629.95(.25) = $157.49
amount to be financed = 472.46
The rest of the question sounds like something from the last century.
A very silly way of doing the financing and it misleads the uninformed.
I will assume they will now take 472.46 , add on $60 to get $532.46
then divide that by 12 to get a monthly payment of
$532.46/12 or $44.37
so to find the rate of interest actually charged:
472.46 = 44.37 (1 - (1+i)^-12)/i
10.64773576 i = (1 - (1+i)^-20)
an extremely difficult equation to solve
I will use Wolfram to attempt it.
(had to change the i to x, or else it interpreted i as
√-1 )
I used : 10.6477= (1 - (1+x)^-20)/x
http://www.wolframalpha.com/input/?i=solve+10.6477%3D+%281+-+%281%2Bx%29%5E-20%29%2Fx
and got .06935 as you can see
so the monthly rate is .06935 and the annual rate is .06935(12) = .8322
or 83.22%
( and they burned people at the stake in the middle ages for such practises)
check on my rate
if annual rate is 83.22% , then monthly rate = 6.935% or .06935
let the monthly payment be p
then 472.46 = p( 1 - 1.06935)^-20)/.06935
472.46 = p(10.6477..)
p = 44.37 , (not bad)
I suppose the intent is for the unscrupulous dealer to suggest that the interest is only $60 on $472.46 for 1 year
or 60/472.46 = .12699
or 12.7% interest and telling them it is a lot better than the 18%+ rate that a credit card will charge.
To answer these questions, we need to break down the information given.
1. The total cost of the sofa is $629.95.
2. Tim makes a 25% down payment. To calculate the down payment amount, we can multiply 25% (or 0.25) by the total cost of the sofa: $629.95 * 0.25 = $157.49. Therefore, the down payment is $157.49.
3. The amount financed is the remaining amount after the down payment. To calculate this, we subtract the down payment from the total cost of the sofa: $629.95 - $157.49 = $472.46. So, the amount financed is $472.46.
4. Tim makes 12 payments that include his principal and a $60.00 finance charge. To find the monthly payment amount, we subtract the finance charge from the total payment and then divide it by 12 (the number of payments). The principal amount is the amount financed divided by the number of payments: $472.46 / 12 = $39.37. To find the monthly payment, we add the principal and finance charge: $39.37 + $60.00 = $99.37. So, the monthly payment will be $99.37.
5. At the end of one year, the total payments will be the monthly payment amount multiplied by the number of payments: $99.37 * 12 = $1,192.44. Therefore, the monthly payments will total $1,192.44 after one year.
6. The finance charge for one year divided by the amount financed will give us the APR (Annual Percentage Rate). The finance charge for one year is $60.00 (as given). Therefore, the APR is $60.00 / $472.46 = 0.127 (rounded to three decimal places). To convert this to a percentage, we multiply by 100: 0.127 * 100 = 12.7%. So, the APR on his loan to the nearest tenth is 12.7%.
To find the down payment, we need to calculate 25% of the total cost of the sofa:
Down payment = 25/100 * $629.95 = $157.49
The down payment is $157.49.
To find the amount financed, we subtract the down payment from the total cost of the sofa:
Amount financed = $629.95 - $157.49 = $472.46
The amount financed is $472.46.
To find the monthly payment, we divide the total payments (including principal and finance charge) by the number of payments:
Monthly payment = ($629.95 + $60.00) / 12 = $52.50
The monthly payment will be $52.50.
To find the total monthly payments at the end of one year, we multiply the monthly payment by the number of months:
Total monthly payments = $52.50 * 12 = $630.00
The total monthly payments at the end of one year will be $630.00.
To find the finance charge for one year divided by the amount financed, we can calculate the annual finance rate.
Total finance charge for one year = $60.00 * 12 = $720.00
APR = (Total finance charge for one year / amount financed) * 100
APR = ($720.00 / $472.46) * 100 ≈ 152.4%
The APR on his loan, to the nearest tenth, is 152.4%.