Question

In order to purchase a home, a family borrows $159,000 at 6.5% for 30 years. . Round the answer to the nearest cent

Answer 1

If It is simple interest problem, then we can find Total Amount to be repaid after 30 years.

The principal amount is P = $159,000.

Annual Percentage Rate is 6.5%, so R = 0.065

Time of loan repayment is 30 years, so T = 30

We can use Simple Interest formula to find the interest to be paid at maturity of loan.

Interest = Principal x APR x Time

Interest = PRT

Interest = 159000 x 0.065 x 30

Interest = 310,050

Total Amount to repay = Principal + Interest

Total Amount to repay = 159,000 + 310,050

Total Amount to repay = 469,050 dollars.

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If it is monthly payment problem, then we can use Present Value formula to find the monthly payments to be repaid.

We have loan amount, PV = 159000.

r = 0.065; t = 30 years; k = 12 (compounded monthly).

`PV=Pmt*((1-(1+(r)/(k))^(-kt))/(((r)/(k)))) \\\\159000=Pmt*((1-(1+(0.065)/(12))^(-12*30))/(((0.065)/(12)))) \\\\159000=Pmt*((1-(1.005416667)^(-360))/((0.005416667))) \\\\159000=Pmt*((1-0.143024727)/((0.005416667))) \\\\159000=Pmt*((0.856975272)/(0.005416667)) \\\\159000=Pmt*(158.2108196) \\\\Pmt = (159000)/(158.2108196) =1004.988157 \approx \$1004.99`

So, monthly payments = $1,004.99

Total amount paid over loan period = 1004.99 x 360 = $361,795.74

Total interest paid over the loan period = $202,795.74

Answer 2

The answer is$1006.47

Explanation:

(I think you couldn't attach the table with shows the monthly payments per $1000 mortgage for 30 years so I am taking the value to be 6.33)

A family borrows $159,000 at 6.5% for 30 years to buy a home which means that the given figure above shows us the monthly rent and interest in mortgage of $1000.

If the monthly interest rate for 30 years is 6.33 dollars. and we are to borrow $159,000, we just need to multiply 159 by 6.33:

159 x 6.33 = 1006.47

Therefore the monthly rent for 30 years would be $1006.47