Tom Burke buys a home in Virginia for $139,000. He puts down 30% and obtains a mortgage for 25 years at 12%. The portion of the first payment that covers interest is:

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Mathematics

Wesley Manning

13 July, 05:43

Tom Burke buys a home in Virginia for $139,000. He puts down 30% and obtains a mortgage for 25 years at 12%. The portion of the first payment that covers interest is:

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Key · Answer 1

You didn't specify the periodic payment in your question. I will solve it assuming that payment is made monthly.

Amount owing by Tom = 70% of 139,000 = 0.7 x 139,000 = $97,300

Present Value of an annuity is given by PV = P (1 - (1 + r) ^-n) / r; where P is the periodic (monthly) payment, r is the interest rate = 12%/12 = 1% = 0.01, n is the number of periods = 25 x 12 = 300 months.

97,300 = P (1 - (1 + 0.01) ^-300) / 0.01

P = 973 / (1 - (1.01) ^-300) = 973 / (1 - 0.050534) = 1,024.79

Thus Tom pays $1,024.79 per month.

Interest due for the first month = 0.01 x 97,300 = $973

Therefore, the portion of the first payment that covers the interest is $973