Answer:
It will take 9 months longer to repay this loan
Explanation:
Financial Loan Payments
Let's assume a loan has been received for a present value PV at an interest rate i during n periods. Being R the amount of each payment, then
[tex]\displaystyle PV=R\cdot \frac{1-(1+i)^{-n}}{i}[/tex]
Solving for n we have
[tex]\displaystyle n=-\frac{log\left(1-PV.i/R\right )}{log(1+i)}[/tex]
The first agreement of payment has the following data
[tex]PV=6,800[/tex]
[tex]i=6.75/(12\cdot 100)=0.005625[/tex]
[tex]R=310[/tex]
Computing n
[tex]\displaystyle n=-\frac{log\left(1-6,800\cdot 0.005625/310\right )}{log(1+0.005625)}[/tex]
[tex]n=23.5\approx 24\ months[/tex]
The new agreement changes R to 225, thus
[tex]\displaystyle n=-\frac{log\left(1-6,800\cdot 0.005625/225\right )}{log(1+0.005625)}[/tex]
[tex]n=33.2\approx 33\ months[/tex]
This means that it will take 9 months longer to repay this loan
