Question

Currently, you owe the bank $9,800 for a car loan. The loan has an interest rate of 7.75 percent and monthly payments of $310. Your financial situation recently changed such that you can no longer afford these payments. After talking with your banker and explaining the situation, he has agreed to lower the monthly payments to $225 while keeping the interest rate at 7.75 percent. How much longer will it take you to repay this loan than you had originally planned?

Answer 1

Answer:

It will extend the loan for 15.83 months = 16 more months.

Explanation:

We need to calcualte the difference in time between one option and another:

Original Loan:

$C \times \frac{1-(1+r)^{-time} }{rate} = PV$

C  $310.00

time n

rate 0.0064583 (0.0775annual rate / 12 month per year)

PV $9,800

$310 \times \frac{1-(1+0.0064583)^{-n} }{0.0064583} = 9800$

We rearrenge and solve as much as we can:

$(1+0.0064583)^{-n}= 1-\frac{9800\times0.0064583}{310}$

$(1+0.0064583)^{-n} = 0.79583439$

Now, we solve using logarithmics properties:

$-n= \frac{log0.795834387096774}{log(1+0.0064583)}$

35.47385568

Now we calcualte with the new terms:

C  $225.00

$225 \times \frac{1-(1+0.0064583)^{-n} }{0.0064583} = 9800$

$(1+0.0064583)^{-n}= 1-\frac{9800\times0.0064583}{225}$

$(1+0.0064583)^{-n}= 0.71870516$

$-n= \frac{log0.718705155555555}{log(1+0.0064583)}$

51.30909653

Last step, we solve for the difference:

51.30 - 35.47 = 15.83 = 16 more months