Round 279 to blank estimate the product

Mathematics

1 answer:

Tju [1.3M]3 years ago

3 0

The estimation for 279 would be 280

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Beth is taking out a loan to purchase a new home. She is financing $50,000 for 25 years at an interest rate of 14.25%. What is h

kozerog [31]

The present value (PV) of a loan for n years at r% compounded t times a year where there is equal P periodic payments is given by:

$PV=P\left( \frac{1-\left(1+ \frac{r}{t} \left)^{-nt}}{ \frac{r}{t} } \right)$

Given that Beth is taking out a loan of PV = $50,000 to purchase a new home for n = 25 years at an interest rate of r = 14.25%. Since she is making the payment monthly, t = 12.

Her monthly payment is given by:

$50,000=P\left( \frac{1-\left(1+ \frac{0.1425}{12} \right)^{-25\times12}}{ \frac{0.1425}{12} } \right) \\ \\ =P\left( \frac{1-(1+0.011875)^{-300}}{ 0.011875 } \right)=P\left( \frac{1-(1.011875)^{-300}}{ 0.011875 } \right) \\ \\ =P\left( \frac{1-0.028969}{ 0.011875 } \right)=P\left( \frac{0.971031}{ 0.011875 } \right)=81.770994P \\ \\ \therefore P= \frac{50,000}{81.770994} =\$611.46$

Therefore, her monthly payment is about $611.50

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