Overhaulin'

Calculate Percentages w/Down Payments?

I have a finance problem I am working on and I am trying to figure out if there is a formula for calculating percentages without using the good ole' plug and chug method. For instance... You would like to buy a car. You can afford a car payment of $325 per month. Your bank is willing to extend you a 5-year loan at a rate of 7.75%. Your bank requires you to put a 20% down payment. a)What is the price of the car you can afford The present value comes to $16,123.46. If I were to simply multiply by 1.20 the answer would come to $19,348.16. However, I know the answer is $20,154.33. I know I can just keep plugging in numbers to find the correct answer, but there has to be a formula that I am missing. Anyone help?

Public Comments

1. You multiplied the present value of the payments by 1.20 to try to get the the total value including the required 20% down payment. But, as you see, that gives you the wrong total. You should have divided the present value by 0.80. You do this because the remaining amount to be financed will be 80% of the total cost of the vehicle. $16,123.46 / 0.80 = $20,154.33 You can test this by calculating $20,154.33 by 20%. This equals $4,030.87. And $20,154.33 - $4,030.87 = $16,123.46 Multiplying 80% of the total by 1.20 gives you an answer that is 96% of the total, not the 100% value you are looking for. Again, you need to divide by 0.80 (80%), not multiply by 1.20