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Fundamentals of Financial Manageme...

15th Edition
Eugene F. Brigham + 1 other
ISBN: 9781337395250

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BuyFindarrow_forward

Fundamentals of Financial Manageme...

15th Edition
Eugene F. Brigham + 1 other
ISBN: 9781337395250
Textbook Problem

LOAN AMORTIZATION AND EAR 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 8% with interest paid monthly. What will be the monthly loan payment? What will be the loan’s EAR?

Summary Introduction

To determine: The monthly loan payment and the effective annual rate.

Introduction:

Amortized Loans:

The amortized loans are the loans which are paid in equal installments and in fixed intervals. The installments paid has both the amount of principal and the amount of interest.

Effective Annual Rate:

The effective annual rate is the rate at which a loan or investment is actually borrowed or earned. The effective annual rate is used to compare different financial instruments. This rate is also called as the effective rate or the effective interest rate.

Explanation

Calculation of monthly installment:

Given,

The amount of loan is $40,000.

The rate of interest is 8%.

The time period is 5 years and hence the number of periods is 60 months.

The formula to calculate the monthly payment is:

C=PV×I1(1+I)N

Where,

  • PV is the present value,
  • C is the monthly payment,
  • I is the interest rate and,
  • N is the time period.

Substitute $40,000 for PV, 60 for N, and 8% for I in the above formula.

C=$40,000×0.08121(1+0.0812)60=$266.6710

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