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4 years ago

Aphrodite took out a 30-year loan from her bank for $170,000 at an APR of

Mathematics

1 answer:

horsena [70]4 years ago

8 0

Answer:

A. $3246.74

Step-by-step explanation:

The monthly payment can be found from the amortization formula.

A = P(r/n)/(1 -(1 +r/n)^(-nt))

where P is the principal amount, r is the annual rate compounded n times per year for t years.

Filling in the values, we compute the monthly payment to be ...

A = $170,000(.072/12)/(1 -(1 +.072/12)^(-12·30)) = $1153.94

The remaining balance after t years will be ...

B = P(1 +r/n)^(nt) -A((1 +r/n)^(nt) -1)/(r/n)

For the given initial principal and the computed payment, after 18 years, the balance will be ...

B = $170000(1 +.072/12)^(12·18) -$1153.94((1 +.072/12)^(12·18) -1)/(.072/12)

B = $111,054.71

The prepayment penalty appears to be ...

(r/2)(0.80B) = (.072/2)(0.80)($111,054.71) = $3,198.38

The closest listed answer choice is ...

A. $3246.74

_____

Please ask your teacher how to get the answer, since none of the offered choices appear to be correct.

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