Question

You owe $6,800 on a car loan that has an interest rate of 6.75 percent and monthly payments of $310. You lost your job and your new job pays less, so your lender just agreed to lower the monthly payments to $225 while keeping the interest rate at 6.75 percent. How much longer will it take you to repay this loan than you had originally planned

Answer 1

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

$\displaystyle PV=R\cdot \frac{1-(1+i)^{-n}}{i}$

Solving for n we have

$\displaystyle n=-\frac{log\left(1-PV.i/R\right )}{log(1+i)}$

The first agreement of payment has the following data

$PV=6,800$

$i=6.75/(12\cdot 100)=0.005625$

$R=310$

Computing n

$\displaystyle n=-\frac{log\left(1-6,800\cdot 0.005625/310\right )}{log(1+0.005625)}$

$n=23.5\approx 24\ months$

The new agreement changes R to 225, thus

$\displaystyle n=-\frac{log\left(1-6,800\cdot 0.005625/225\right )}{log(1+0.005625)}$

$n=33.2\approx 33\ months$

This means that it will take 9 months longer to repay this loan