## Related questions with answers

Abby and Jason are building a new house. They obtained a construction loan of $100,000, which will be rolled over into a conventional 20-year mortgage when the house is completed in 14 months. Simple interest of$$$\frac{1}{2}$% per month will be charged on the construction loan. The 20-year mortgage will carry a 6% interest rate with monthly payments. What is the monthly payment that Abby and Jason will make? If they make each payment as scheduled for the life of the 20-year mortgage, how much total interest will they pay on the house?

Solutions

VerifiedIn this problem, we are asked to calculate the monthly payment of the couple towards the mortgage and the total interest required to pay for the house.

With simple interest of $i=0.5\%$ per month, over 14 months,

the interest on the construction loan will be

$F=Pin= 100,000(0.005\cdot 14)={{\$}} 7,000$

The present worth of the mortgage is ${{\$}} 107,000.$

The monthly rate is $i=\displaystyle \frac{6\%}{12}=0.5\%$

$n=20\times 12=240$

$A=P[\displaystyle \frac{i(1+i)^{n}}{(1+i)^{n}-1}]=P(A/P, i, n)$

$A=107,000(A/P, 0.5\%, 240)=107,000(0.00716)={{\$}} 766.12$

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