Answered: Find the monthly payment needed to…

Pfin (with Mindtap, 1 Term Printed Access Card) (mindtap Course List)

7th Edition

ISBN:9780357033609

Author:Randall Billingsley, Lawrence J. Gitman, Michael D. Joehnk

Publisher:Randall Billingsley, Lawrence J. Gitman, Michael D. Joehnk

Chapter5: Making Automobile And Housing Decisions

Section: Chapter Questions

Problem 7FPE

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Question

Find the monthly payment needed to amortize a typical $105,000 mortgage loan amortized over 30 years at an annual interest rate of 4.5% compounded monthly. (Round your answers to the nearest cent.)
$

Find the total interest paid on the loan.
$

Expert Solution

Step 1

We need to determine the monthly payment as well as the interest component.

Given,

Interest rate = 4.5% compounded monthly

= 4.5%/12 = 0.375% monthly

Period = 30 years

= 30*12 = 360 months

Loan = 105000

Step 2

This can be done in Excel

PMT(4.5%/12,30*12,-105000 )

=$532.02

Using formula,

$M o n t h l y p a y m e n t = P r i n c i p a l * \frac{i (1 + i)^{n}}{(1 + i)^{n} - 1} w h e r e i = m o n t h l y i n t e r e s t r a t e n = n u m b e r o f m o n t h s$

$M = 105000 * \frac{. 00375 {(1.00375)}^{360}}{{(1.00375)}^{360} - 1}$

=532.19

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