Question

Tom Henderson takes out a $120,000 mortgage. He paid 1.6% of the loan amount in closing costs and $8,962.49 in total interest the first year of the loan. What are Tom's closing costs? $ If the APR is (interest for one year plus closing costs) ÷ (amount financed), what was the APR for that year? % If the APR is (interest only for one year) ÷ (amount financed), what was the APR (to the nearest tenth) for that year? % NEXT QUESTION ASK FOR HELP TURN IT IN

Answer 1

Given

A loan amount of $120,000

Closing costs of 1.6% times the loan amount

First-year interest of $8962.49

APR₁ = (first-year interest + closing costs)/(loan amount)

APR₂ = (first-year interest)/(loan amount)

Find

APR₁

APR₂

Solution

It can be easier to start with APR₂.

... APR₂ = interest/principal = 8962.49/120,000 ≈ 7.5%

Then APR₁ can be found by adding the percentage of loan amount that was used to compute closing costs: 1.6%

... APR₁ = APR₂ + 1.6% = 9.1%

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Perhaps you see that

... APR₁ = (interest + closing cost)/principal = interest/principal + closing cost/principal

But the closing costs are 1.6%×principal, so we have

... APR₁ = interest/principal + (1.6%×principal)/principal

... ... = interest/principal + 1.6%

... ... = APR₂ + 1.6%

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If the APR includes closing costs, it is 9.1%.

If the APR does not include closing costs, it is 7.5%.