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Darya [45]
3 years ago
12

Suppose you take out a home mortgage for ​$180.000 at a monthly interest rate of 0.4​%. If you make payments of ​$1000​/month, a

fter how many months will the loan balance be​ zero? Estimate the answer by graphing the sequence of loan balances and then obtain an exact answer.
Business
1 answer:
cluponka [151]3 years ago
7 0

Answer:

<u>time = 318.77</u>

It will be after 318 months

Explanation:

We are asked to find the time of an annuity of 1,000 monthly payment

which present value is 180,000

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

C = 1000

rate = 0.004

time ??

PV = 180,000

1,000 \times \frac{1-(1+0.004)^{-time} }{0.004} = 180,000\\

We clear out the dividend:

1-(1+0.004)^{-time} = \frac{180,000\times 0.004}{1,000}\\

Then we clear the power up, notice it is negative, so we have to multiply by (-1)

(-1) \times (-(1+0.004)^{-time}) = (-1) \times (0.72 - 1)}\\

1.004^{-time} = 0.28

We now use logarithmics to solve for time

log_{1.004}0.28 = \frac{log0.28}{log1.004} = -318.87 =-time

<u>time = 319</u>

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