Question

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?

Answer 1

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