Question

You find that the going rate for a home mortgage with a term of 30 years is 4.5% APR. The lending agency says that based on your income, your monthly payment can be at most $750 . How much can you borrow?

Answer 1

Question #43239, Math, Algebra

You find that the going rate for a home mortgage with a term of 30 years is 4.5% APR. The lending agency says that based on your income, your monthly payment can be at most $750. How much can you borrow?

Answer.

In the case of a loan with no fees, the amortization schedule would be :

$$p = P _ {0} \frac {r (1 + r) ^ {n}}{(1 + r) ^ {n} - 1}$$

where:

$P_0$ is the initial principal

$r$ is the percentage rate used each payment

$n$ is the number of payments.

In our case: $n = 30 * 12 = 360$,

$$(1 + r) ^ {12} = 1.045 \rightarrow r = 0.003675,$$ $$p = \$750.$$

So,

$$P _ {0} = p \frac {(1 + r) ^ {n} - 1}{r (1 + r) ^ {n}} = 750 \frac {(1 + 0.003675) ^ {360} - 1}{0.003675 (1 + 0.003675) ^ {360}} = 149595.83.$$

So you can borrow $150,000.

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