Question

What would be the monthly mortgage payments for each of the following situations?

A $64,000, 15-year loan at 7.0 percent APR compounded semi-annually

A $140,000, 25-year loan at 5.5 percent APR compounded semi-annually

A $104,000, 20-year loan at 4.0 percent APR compounded semi-annually

Answer 1

Part A)

To determine the amount of payment, we first need to find the effective rate of interest as below:

Effective Rate of Interest = (1+Interest Rate/Compounding Frequency)^Compounding Frequency - 1 = (1+7%/2)^(2) - 1 = 7.1225%

Now, we can calculate the amount of monthly payment with the use of formula given below:

Payment = (Rate of Interest*Present Value of Loan)/(1-(1+Rate of Interest)^(-Period))

Here, Rate of Interest = 7.1225%/12, Present Value of Loan = $64,000 and Period = 15*12 = 180

Using these values in the above formula for Payment, we get,

Monthly Payment = (7.1225%/12*64,000)/(1-(1+7.1225%/12)^(-180)) = $579.64

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Part 2)

To determine the amount of payment, we first need to find the effective rate of interest as below:

Effective Rate of Interest = (1+Interest Rate/Compounding Frequency)^Compounding Frequency - 1 = (1+5.5%/2)^(2) - 1 = 5.5756%

Now, we can calculate the amount of monthly payment with the use of formula given below:

Payment = (Rate of Interest*Present Value of Loan)/(1-(1+Rate of Interest)^(-Period))

Here, Rate of Interest = 5.5756%/12, Present Value of Loan = $140,000 and Period = 25*12 = 300

Using these values in the above formula for Payment, we get,

Monthly Payment = (5.5756%/12*140,000)/(1-(1+5.5756%/12)^(-300)) = $866.06

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Part 3)

To determine the amount of payment, we first need to find the effective rate of interest as below:

Effective Rate of Interest = (1+Interest Rate/Compounding Frequency)^Compounding Frequency - 1 = (1+4%/2)^(2) - 1 = 4.04%

Now, we can calculate the amount of monthly payment with the use of formula given below:

Payment = (Rate of Interest*Present Value of Loan)/(1-(1+Rate of Interest)^(-Period))

Here, Rate of Interest = 4.04%/12, Present Value of Loan = $104,000 and Period = 20*12 = 240

Using these values in the above formula for Payment, we get,

Monthly Payment = (4.04%/12*104,000)/(1-(1+4.04%/12)^(-240)) = $632.41