Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Chapter1: Investments: Background And Issues
Section: Chapter Questions
Problem 1PS
Related questions
Question
The final payment the bank will require you to make is
$
Transcribed Image Text:**Financial Planning: Loan Payment Analysis**
You have a loan outstanding that requires making nine annual payments of $3,000 each at the end of the next nine years. Your bank has offered to allow you to skip making the next eight payments in lieu of making one large payment at the end of the loan's term in nine years.
**Key Question:**
If the interest rate on the loan is 8%, what final payment will the bank require you to make so that it is indifferent to the two forms of payment?
**Explanation:**
- **Annual Payments:** Regular payments made annually.
- **Interest Rate:** The percentage charged on the loan, here at 8%.
- **Final Payment Option:** Instead of smaller periodic payments, a larger single payment is made at the end of the term.
To find the equivalent final payment, the concept of the present value and future value of annuities will be used, factoring in the interest rate.
Expert Solution
Step 1: Formula of Future Value of Annuity
This is the case of Future Value of annuity
Future Value of annuity
= PMT * [ {(1+ r)n -1}/r]
where PMT = annual installment
r = Interest rate
n = number of payments
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