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aev [14]
3 years ago
10

House Loan. Suppose you take out a home mortgage for $180,000 at a monthly interest rate of 0.5%. If you make payments of $1000/

month, after how many months will the loan balance be zero?
Business
1 answer:
zzz [600]3 years ago
7 0

Answer:

It will be after 462 months

Explanation:

We use the annuity formula for present value

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

We post our know values and start solving for time:

1000 * \frac{1-(1+0.005)^{-time} }{0.005} = 180,000

First we clear the dividend:

1-(1+0.005)^{-time} = 180,000/1000\times 0.005

Then we clear for the power

(1.005)^{-time} = 1-0.9

We set up the formula using logarithmic

log_{1.005}\: 0.1 = -time

And use logarithmic properties to solve for time:

\frac{log\:0.1}{log\:1.005} = -time

-461.6673541 = -time

time 462 months

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