<h3>Given</h3>
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)
<h3>Find</h3>
APR₁
APR₂
<h3>Solution</h3>
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%.
