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Robert is selling his home to his good friend, Lisa. Robert is selling his waterfront multi-storey home for $3,950,000, and he will take back a mortgage for $2,000,000 at a contract rate of j2 = 4.5%, with a 25-year amortization period, a 3-year term, and monthly payments rounded up to the next higher $10. how much will Lisa owe Robert at the end of the 3-year term? Round your final answer to the nearest dollar.

Sagot :

Sqdancefanidn

Answer:

  $1,860,753

Step-by-step explanation:

You want to know the amount remaining on a $2M mortgage at 4.5% after 3 years if payments are rounded to the next higher $10.

Payment amount

The loan amortization formula tells you the monthly payment amount on a loan of P at interest rate r for t years is ...

  [tex]A=P\cdot\dfrac{r/12}{1-(1+r/12)^{-12t}}\\\\\\A=2\,000\,000\cdot\dfrac{0.00375}{1-1.00375^{-300}}\approx11\,116.65[/tex]

Rounded to the next higher $10, Lisa's monthly payment is $11,120.

Remaining balance

The remaining balance on a loan of P after m payments of p on a loan with monthly interest rate r is ...

  [tex]B=P(1+r)^m-p\cdot\dfrac{(1+r)^m-1}{r}\\\\\\B=2\,000\,000(1.00375^{36})-11\,120\dfrac{(1.00375^{36}-1)}{0.00375}\\\\\\B\approx 2\,288\,495.66-427\,742.91=1\,860\,752.75[/tex]

At the end of the 3-year term, Lisa will owe $1,860,753.

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Additional comment

We assume Lisa has already paid the difference between the $3.95M sale price and the $2M loan value.

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