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4 years ago

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You have an outstanding student loan with required payments of $500 per month for the next four years. The interest rate on the

loan is 9% APR (compounded monthly). Now that you realize your best investment is to prepay your student loan, you decide to prepay as much as you can each month. Looking at your budget, you can afford to pay an extra $ 175 a month in addition to your required monthly payments of $500, or $675 in total each month. How long will it take you to pay off the loan?

1 answer:

irina [24]4 years ago

5 0

Answer:

<em>n = 33.8108479</em>

Explanation:

We will calculate the current principal

And then calculate the time period it takes with a higher payment of 675 dollars per month:

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

C $ 500

time 48 ( 4 years x 12 months per year)

rate 0.0075 (9% annual divide by 12 months)

$500 \times \frac{1-(1+0.0075)^{-48} }{0.0075} = PV\\$

PV $20,092.3909

Now we recalculate n:

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

C $675.00

time n

rate 0.0075

PV $20,092.3900

$675 \times \frac{1-(1+0.0075)^{-n} }{0.0075} = 20092.39\\$

<u>from the annuity formula we solve as we can until arrive at this situation:</u>

$(1+0.0075)^{-n}= 1-\frac{20092.39\times0.0075}{675}$

$(1+0.0075)^{-n}= 0.77675122$

<u>We use logarithmics properties to solve for n:</u>

$-n= \frac{log0.77675122}{log(1+0.0075)}$

<em>n = 33.8108479</em>

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Answer:

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Explanation:

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