Question 1082358: Ben bought a new car and took out a loan for $20,000 with a monthly interest of 0.5%. If Ben pays $150 per month, what is the balance after 3 months?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the loan is 20,000 dollars.
the monthly interest rate is .5%.
he pays 150 dollars per month.
you take the remaining balance at the beginning of each month and multiply it by 1.005 and then subtract the monthly payment of 150 to get the remaining balance
you will get:
beginning of month 1 20,000
end of month 1 20,000 * 1.005 - 150 = 19,950
end of month 2 19,950 * 1.005 - 150 = 19,899.75
end of month 3 19,899.75 * 1.005 - 150 = 19,849.24875
you would round this off to 19,849.25 remaining balance of the loan after 3 months.
the monthly interest rate of .5% is divided by 100 to get a monthly interest rate of .005
the balance at the end of each month is equal to the balance at the beginning of each month plus .005 * the balance the balance at the beginning of that month.
if the balance at the beginning of the month is equal to x, then the balance at the end of that month is equal to x + .005 * x which is equal to 1.005 * x.
therefore, the balance at the end of each month is equal to the balance at the beginning of each month * 1.005.
the monthly payment is then subtracted from the balance at the end of each month because the payment is assumed to occur at the end of each month.
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