SOLUTION: A simple-interest account contained $780 eight months after it was opened, and it contained $855 ten months after that. Find the original amount in the account.

Question 643216: A simple-interest account contained $780 eight months after it was opened, and it contained $855 ten months after that. Find the original amount in the account.

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
simple interest means no compounding.
this means your interest per month is going to be the same every month.
the formula for simple interest is:
f = p * i * n
i is the interest rate.
p * i is the interest
p is the principal.
f is the future value.
n is the number of time periods.
just solve for the monthly interest and work your way back.
in your problem:
account contains 780 after 8 months and contains 855 10 months after that.
in 10 months, the account grew from 780 to 855 which is a growth of 75 dollars.
divide that by 10 months and that becomes 7.5 dollars growth per month.
8 * 7.5 = 60 dollars.
subtract 60 from 780 and you start with 720 dollars 8 months before you had 780.
your original amount is 720 dollars.
your interest per month is 7.5
720 + 8*7.5 = 780 + 10*7.5 = 855.

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