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3 years ago

8

you secure a mortgage to buy a house with a loan of $140,000 at 8.5% for 20 years. answer the following questions about that loa

n for the first two months of payments: a) what is the monthly payment? b)how much of the monthly payment goes toward interest when you submit your first payment? c)what is your balance after the first payment? d) how much of the monthly payment goes toward interest when you submit your second payment? e) what is your balance after the second payment?

1 answer:

Yuri [45]3 years ago

8 0

Answer:

monthly payment $1214.95
1st month's interest $991.67
balance after 1st payment $139,776.72
2nd month's interest $990.09
balance after 2nd payment $139,551.86

Step-by-step explanation:

The monthly interest rate is ...

$\dfrac{8\%}{12}=0.00708\overline{3}$

a) The monthly payment is given by the amortization formula:

A = Pr/(1 -(1+r)^-n)

where r is the monthly interest rate on a loan of amount P for n months.

A = $140,000(0.0070833)/(1 -(1.0070833^-240)) = $1214.95

The monthly payment is $1214.95.

__

b) The amount to interest is the product of the remaining principal and the monthly interest rate.

first month's interest = $140,000·0.0070833 = $991.67

__

c) The balance after the first payment is ...

new balance = $140,000 +991.67 -1214.95 = $139,776.72

__

d) The amount to interest for the second payment is computed the same way:

second month's interest = $139,776.72·0.00708333 = $990.09

__

e) The balance after the second payment is computed the same way:

new balance = $139,776.72 +990.09 -1214.95 = $139,551.86

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To convert the decimal 2.125 to a fraction follow these steps:

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2.125 = 2.125/1

Step 2: Multiply both top and bottom by 10 for every number after the decimal point:

As we have 3 numbers after the decimal point, we multiply both numerator and denominator by 1000. So,

2.125/1 = (2.125 x 1000)/(1 x 1000) = 2125/1000.

Step 3: Simplify (or reduce) the above fraction by dividing both numerator and denominator by the GCD (Greatest Common Divisor) between them. In this case, GCD(2125,1000) = 125. So,

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