Question 1164287: Hi
Frank borrows 8000 dollars for 3 years simple interest at 10% pa. One year into the loan he needs to borrow a further 2500 dollars at 12.5% pa. How much does he owe altogether on these loans after 3 years given no repayments were made.
My answer was 14,125 dollars the textbook says 13,525 dollars.
Thanks
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the formula for simple interest is:
f = p * (1 + r * n)
f is the future value
p is the present value
r is the interest rate per time period
n is the number of time periods.
you have two loans.
the first loan is for 8000 at 10% interest per year for 3 years.
the second loan is for 2500 at 12.5% interest per year for 2 years, starting in the second year of the first loan.
these are two separate loans.
they should not be combined until the end.
the first loan gets you f = 8000 * (1 + .10 * 3) = 10400 due at the end of the third year.
the second loan gets you f = 2500 * (1 + .125 * 2) = 3125 due at the end of the second year which coincides with the end of the third year for the firsts loan.
add them together and your total debt is 13525 at the end of the third year of the first loan.
what you did was the following, as far as i can tell.
8000 * 1.1 = 8800
then you added 2500 to that to get 11300
then you did the following:
11300 * (1 + .125 * 2) = 14235.
you combined the loans together after the first year and then charged both of them 12.5% interest for the next two years.
your first loan was charged 10% for the first year and then 12.5% for the next two year.
this is not consistent with the requirements of the first loan.
the first loan needed to be at 10% for all 3 years.
the second loan was a separate loan at 12.5% running concurrently with the first loan at 10% per year for the remaining two years of the first loan.
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