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
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Question
A store amortizes a $75,000 loan at 10% compounded quarterly with quartlerly payments of $2985.72 for 10 years. How much will be the unpaid balance after 7 years?
Expert Solution
Step 1 Given Loan amount = 75000, r=10% per annum
So per quarter k = 10/4= 2.5%, Loan Maturity = 10 years= 10* 4= 40 times = n
We must know the Principal Value (Unpaid value) after end of the 7th year.
Given quarterly payment = 2985.72
Or It may be calculated as -
Take quaterly payment is x, So PVIFA,( k=2.5%,n=40)= 75000
PVIFA,2.5%,40= (1+k)^n-1 /(1+k)^n*k= 1.025 ^40-1 /1.025 ^40= (2.6850-1)/ 2.6850*0.025=25.10
So quarter payment= 25.1027751x= 75000
so x =75000/2.51195=2985.72 Little deviation from your answer =
2985.72
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