Question

Annuity Payment and EAR

You want to buy a car, and a local bank will lend you $30,000.
The loan would be fully amortized over 3 years (36 months), and the
nominal interest rate would be 6% with interest paid monthly. What
is the monthly loan payment? Do not round intermediate
calculations. Round your answer to the nearest cent.

$

What is the loan's EFF%? Round your answer to two decimal
places.

%

Answer #1

Answer a.

Amount borrowed = $30,000

Period = 3 years or 36 months

Annual interest rate = 6%

Monthly interest rate = 0.50%

Let monthly payment be $x

$30,000 = $x/1.005 + $x/1.005^2 + ... + $x/1.005^35 +
$x/1.005^36

$30,000 = $x * (1 - (1/1.005)^36) / 0.005

$30,000 = $x * 32.871016

$x = $912.66

Monthly payment = $912.66

Answer b.

Effective annual rate = (1 + Monthly interest rate)^12 - 1

Effective annual rate = (1 + 0.005)^12 - 1

Effective annual rate = 1.0617 - 1

Effective annual rate = 0.0617 or 6.17%

Problem 4-8
Annuity Payment and EAR
You want to buy a car, and a local bank will lend you $10,000.
The loan would be fully amortized over 5 years (60 months), and the
nominal interest rate would be 10% with interest paid monthly. What
is the monthly loan payment? Do not round intermediate
calculations. Round your answer to the nearest cent.
$
What is the loan's EFF%? Round your answer to two decimal
places.
%

You want to buy a car, and a local bank will lend you $20,000.
The loan would be fully amortized over 3 years (36 months), and the
nominal interest rate would be 6%, with interest paid monthly. What
is the monthly loan payment? Do not round intermediate
calculations. Round your answer to the nearest cent.
$ ---------------
What is the loan's EFF%? Do not round intermediate calculations.
Round your answer to two decimal places.
-----------%

You want to buy a car, and a local bank will lend you $10,000.
The loan would be fully amortized over 3 years (36 months), and the
nominal interest rate would be 15%, with interest paid monthly.
What is the monthly loan payment? What is the loan's EFF%?

You want to buy a car, and a local bank will lend you $35,000.
The loan will be fully amortized over 5 years (60 months), and the
nominal interest rate will be 10% with interest paid monthly. What
will be the monthly loan payment? What will be the loan's EAR? Do
not round intermediate calculations. Round your answer for the
monthly loan payment to the nearest cent and for EAR to two decimal
places.

You want to buy a car, and a local bank will lend you $40,000.
The loan will be fully amortized over 5 years (60 months), and the
nominal interest rate will be 4% with interest paid monthly. What
will be the monthly loan payment? What will be the loan's EAR? Do
not round intermediate calculations. Round your answer for the
monthly loan payment to the nearest cent and for EAR to two decimal
places.

You want to buy a car, and a local bank will lend you $25,000.
The loan will be fully amortized over 5 years (60 months), and the
nominal interest rate will be 9% with interest paid monthly. What
will be the monthly loan payment? Do not round intermediate steps.
Round your answer to the nearest cent. $
What will be the loan's EAR? Do not round intermediate steps.
Round your answer to two decimal places. %

You want to buy a car, and a local bank will lend you $15,000.
The loan will be fully amortized over 5 years (60 months), and the
nominal interest rate will be 11% with interest paid monthly.
What will be the monthly loan payment? Do not round intermediate
steps. Round your answer to the nearest cent.
$
What will be the loan's EAR? Do not round intermediate steps.
Round your answer to two decimal places.
%

You want to buy a car, and a local bank will lend you $10,000.
The loan will be fully amortized over 5 years (60 months), and the
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What will be the monthly loan payment? Do not round intermediate
steps. Round your answer to the nearest cent.
What will be the loan's EAR? Do not round intermediate steps.
Round your answer to two decimal places.

You want to buy a car, and a local bank will lend you $30,000.
The loan will be fully amortized over 3 years (60 months), and the
nominal interest rate will be 5.25% with interest paid monthly.
What will be the monthly loan payment? What will be the
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You want to buy a car, and a local bank will lend you $35,000.
The loan would be fully amortized over 5 years (60 months), and the
nominal interest rate would be 15%, with interest paid monthly.
What is the monthly loan payment? Do not round intermediate
calculations. Round your answer to the nearest cent.

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