Time value of money, should i calculate the effective annual rate for this question

[vitalstrike82]

Hi, below is a question from qbank:
An individual borrows $200,000 to buy a house with a 30-year mortgage requiring payments to be made at the end of each month. The interest rate is 8%, compounded monthly. What is the monthly mortgage payment?
A) $1,467.53.
B) $2,142.39.
C) $1,480.46.
Your answer: A was correct!
With PV = 200,000; N = 30 × 12 = 360; I/Y = 8/12; CPT → PMT = $1,467.53.
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Initially i calculate this qns using the effective annual rate which i calculate is 8.3%.
Then i input these values into the calculator:
With PV = 200,000; N = 360; I/Y = 8.3/12; CPT → PMT = $1,509.569
Actually do i need to compute the interest rate to the effective annual rate? I feel that i makes sense to calculate the effective annual rate and input into the calculation.
Any views?
thanks

 

[anish]

No you don’t need to. You use 1/12 of the stated annual rate i.e. 1/12 of 8
Effective annual rate is used when you need to find out that effectively how much did he pay till the end of the year including compounding i.e. including the interest he lost on the initial payments i.e. he lost 11 month interest on the payment he made in Jan so value of 1467 is a little more by the end of the year. Hence effective interest rate is a little higher. But you don’t have to worry about that here since you only need to find out his monthly payments.

 

[vitalstrike82]

oh i see.. thanks for the explanation