Question

What is the monthly payment for a 30-year mortgage with a 3.00% APY? How much of the first payment goes toward reducing the principal amount owed?

Answer 1

Given

Let the loan Amount = $ 100000

Mortgage period = 30 Years

APY = 3%

Interest per Month = 3%/12 = 0.25%

No.of Monthly installments = 30*12= 360 Installments

Computation of Monthly Installment.:

We know that PV of Ordinary Annuity = C [ { 1-( 1+i)^-n } /i]

Here C = Cash flow per period

I = Interest rate per period

n = No.of payments

We know that Present value of the future cash flows is equal to the loan amount.

$ 100000=C [ { 1-(1+0.0025)^-360} /0.0025]

$ 100000= C [ { 1-( 1.0025)^-360} /0.0025]

$ 100000=C [ { 1-0.407027} /0.0025]

$ 100000= C [ 0.592973/0.0025]

$ 100000/237.1894 =C

C = $ 421.604

Hence the Monthly loan Payment = $ 421.604

S..No	Opening Balance	Interest @ 0.25%( Opening Balance *0.25%)	Total outstanding Balance	Amount paid	Closing Balance [ Total outstanding Balance -Amount paidd]
1	$100,000	$250.00	$100,250.00	$421.60	$171.60

Out of $ 421.60, the amount allocaed to interest is $ 250

Amount allocated to principal = $ 421.60-$ 250=$ 171.60

Hence $ 171.60 is attributed to the principle.

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