Answer:
D. 543.46
Step-by-step explanation:
The formula for the remaining balance on the loan is ...
A = P(1 +r)^n +p((1 -(1 +r)^n)/r)
where P is the principal, p is the monthly payment, r is the monthly interest rate, and n is the number of months.
We have P=135,000, p = TBD, r = 3.6%/12 = .003, n = 20×12 = 240.
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The monthly payment is given by the same formula by setting A=0. In this case, n is 25 years, or 300 payments. Solving for p, we get, ...
p = Pr(1 +r)^n/((1 +r)^n -1) = Pr/(1 -(1 +r)^-n)
So, the monthly payment is ...
p = 135,000×0.003/(1 -1.003^-300) = 683.10
Using this value in the formula for remaining balance, we get ...
A = 135000(1.003^240) +683.10((1 -1.003^240)/0.003) = 37,459.20
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80% of this balance is 29,967.36. The answer choices only make sense if we assume the interest penalty is equivalent to the interest being compounded monthly:
$29,967.36 × (1.003^6 -1) = $543.47
The closest match among answer choices is ...
D. 543.46
