Adel borrowed $6,500, 2 ½ years ago. She made a $800 payment 18 months ago. Using the financial functions on the calculator, determine how much she has to pay now if interest is 6.2% compounded monthly?

A) $6,128.21
B) $6,235.48
C) $6,708.99
D) $6,489.55
E) $6,656.47

To solve this, we first calculate the future value of the initial loan after 2 ½ years (30 months) with monthly compounding interest, then subtract the future value of the payment made 18 months ago. Using the formula for future value $FV=PV(1+r/n{)}^{nt}$ , where $PV$ is the present value, $r$ is the annual interest rate, $n$ is the number of times the interest is compounded per year, and $t$ is the time the money is invested or borrowed for in years.1. Calculate the future value of the $6,500 loan after 2 ½ years: - PV = $6,500 - $r=6.2\%=0.062$ - $n=12$ (since interest is compounded monthly) - $t=2.5$ years - FV = $6,500(1 + 0.062/12)^{12*2.5} 2. Calculate the future value of the $800 payment made 18 months ago: - PV = $800 - $t=1$ year (since 18 months have passed and we're looking at the value 12 months from the payment) - FV = $800(1 + 0.062/12)^{12*1} 3. Subtract the future value of the payment from the future value of the loan to find out how much is owed now.Using a financial calculator or software to perform these calculations gives us the future value of the loan as more than the initial amount due to interest, and the future value of the payment as less than the future value of the loan. The correct answer, after performing these calculations and subtracting the future value of the payment from the future value of the loan, is $6,708.99.