The correct statement is that the amount of Tyrell's down payment for the house costing $186,500 for a period of 30 years at an interest rate of 6.5% will be $18650. So, the correct option is B.
The calculation can be done by obtaining the future value of the mortgaged house loan for the period as per the values given in the information above.
Calculation of down payment.
- The total payment of the loan can be calculated as using the given formula to apply available values.
- [tex]\rm Future\ Value= 186500(1+ \dfrac{0.065}{1})^3^0 ^x^1\\\\\rm Future\ Value= \$424370.47[/tex]
- However, it has been provided that the monthly payments are as 1060.93 USD. So, the total payment excluding down payment will be,
- [tex]\rm Total\ Annuity\ Paid= 1060.93\ x\ 360\\\\\rm Total\ Annuity\ Paid= \$381934.8[/tex]
- So the value of down payment will be,
- [tex]\rm Down\ Payment= 424370.47-381934.8\ USD\\\\\rm Down\ Payment= 18650\ USD[/tex]
- It is to be noted that the rate of interest over the down payment amount has also been reduced and hence the amount comes as $18,650.
Hence, the correct option is B that the down payment amount for Tyrell's house will be $18,650.
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