Calculating future value and Present Value I have been stuck on this one for hours ... not too great at math can someone help. Thanks. Isaac borrowed $\$4000$ at $11.5\%$ compounded quarterly $5.5$ years ago. One year ago he made a payment of $\$1500$. What amount will extinguish the loan today? I've tried a bunch of different approaches, none were right. From what I understand we should calculate the FV for $4.5$ years when $PV=\$4000$ then subtract $\$1500$ from answer and calculate FV for one more year. But still no luck..

First: The "value" of the loan after $4.5$ years would be $$ FV(4.5) = 4,000\left(1 + \frac{0.115}{4}\right)^{4\cdot 4.5}. $$ Now then after the $4.5$ years you would subtract $1,500$ from the debt and the add one years extra interest to what is left over. This will give you the future value after the $5.5$ years:

$$ (FV(4.5) - 1500)*(1 + \frac{0.115}{4})^{4\cdot 1} $$

So this is equivalent to making a new loan of $FV(4.5)$ and then calculate what that load is "worth" after $1$ year with $11.5\%$ compounded quarterly.