Question

What are your payments on a 11-year, $130,000 loan at 9.75% compounded semi-annually assuming the payments are made monthly?

Question 16 options:

$1,436

$1,475

$1,515

$1,555

$1,595

Answer 1

Given interest rate = 9.75% compounded semiannually,

So, Effective annual rate = (1+APR/2)^2 - 1 = (1+0.0975/2)^2 - 1 = 9.99%

Since payment are monthly, we need to calculate APR compounded monthly,

So, APR compounded monthly = 12*((1+EAR)^(1/12) -1) = 12*((1.0999^(1/12))-1) = 9.56%

Given about loan is

Loan amount PV = $130000

time period t = 11 years

n = 12 months in a years

So, Monthly payment PMT using ordinary annuity formula is

PMT = PV*(r/n)/(1 - (1+r/n)^(-n*t)) = 130000*(0.0956/12)/(1 - (1+0.0956/12)^(-12*11)) = $1595.388

The answer is $1595.

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