A used motorcycle is priced at 3,438.if you borrow the money foe the motorcycle,your payments will be $165 a month for 24 months.how much will you save by paying cash?
165 * 24 = ?
Subtract 3,438 from the above product.
Yes, that is the desired answer.
However it is not really nearly that easy.
Assume you have 3438 in your back pocket.
If you take that loan you will pay a total of 3960
so the easy answer is you save
522
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Now the hard part.
that is 261 per year interest
261/3438 = 7.6 percent
If you can make more than 7.6 percent interest with that money in your back pocket , you come out ahead with the loan.
It gets even more complicated when you consider that more than likely compound interest would have been used.
So at what rate are 24 payments equivalent to a present value of 3438 ?
165(1 - (1+x)^-24)/x = 3438, where x is the monthly rate
tough to solve, used Wolfram:
http://www.wolframalpha.com/input/?i=165(1+-+(1%2Bx)%5E-24)%2Fx+%3D+3438
x = .0116316
annual rate = 12(.0116316) = appr 13.96%
So the real rate of the loan is 14%
As Damon says, unless you can invest your $3438 at more than 14%, pay cash
To calculate how much you would save by paying cash for the used motorcycle, we need to compare the cost of borrowing with the total cash price.
First, let's find out how much you would pay if you borrow the money. The monthly payment is $165, and you will make payments for 24 months. So, the total amount you would pay if you borrow the money would be:
Total amount paid = Monthly payment x Number of months
Total amount paid = $165 x 24
Total amount paid = $3,960
Now, let's calculate how much you would save by paying cash. The total cash price of the motorcycle is $3,438. Therefore, the savings would be:
Savings = Total amount paid (if borrowed) - Total cash price
Savings = $3,960 - $3,438
Savings = $522
Therefore, you would save $522 by paying cash for the used motorcycle.