Present Value of an Ordinary Annuity 1- (1 + i) PV = PMT- i where PV = present value of all payments PMT = periodic payment i= rate per period (written as a decimal) n= number of periods %3D Note: Payments are made at the end of each period. a. To find the monthly payment, use the formula for the present value of an ordinary annuity and solve it for PMT. Now find the total interest paid. Total interest paid = (amount of all payments) - (initial loan) Present Value of an Ordinary Annuity -n 1-(1 + i) PV = PMT- where PV = present value of all payments PMT = periodic payment i= rate per period (written as a decimal) n= number of periods %3D %3D Note: Payments are made at the end of each period. b. To find out how long it will take to pay off the mortgage by paying an extra $100 a month requires the use of a new formula that has n, the number of periods, as the dependent variable. We want to start with the formula for the present value of an ordinary annuity and then use logarithms to solve it for n. 1-(1+ i) -n PV = PMT: Original equaton. i• PV log 1 1-(1+ i)" PMT Therefore, solving PV = PMT for n yields n= log(1 + i) Of the three variables on the right side of the new equation for n, the PV amd i will stay the PMT will change. Now find the total interest paid. Total interest paid = (amount of all payments) – (initial loan)
Present Value of an Ordinary Annuity 1- (1 + i) PV = PMT- i where PV = present value of all payments PMT = periodic payment i= rate per period (written as a decimal) n= number of periods %3D Note: Payments are made at the end of each period. a. To find the monthly payment, use the formula for the present value of an ordinary annuity and solve it for PMT. Now find the total interest paid. Total interest paid = (amount of all payments) - (initial loan) Present Value of an Ordinary Annuity -n 1-(1 + i) PV = PMT- where PV = present value of all payments PMT = periodic payment i= rate per period (written as a decimal) n= number of periods %3D %3D Note: Payments are made at the end of each period. b. To find out how long it will take to pay off the mortgage by paying an extra $100 a month requires the use of a new formula that has n, the number of periods, as the dependent variable. We want to start with the formula for the present value of an ordinary annuity and then use logarithms to solve it for n. 1-(1+ i) -n PV = PMT: Original equaton. i• PV log 1 1-(1+ i)" PMT Therefore, solving PV = PMT for n yields n= log(1 + i) Of the three variables on the right side of the new equation for n, the PV amd i will stay the PMT will change. Now find the total interest paid. Total interest paid = (amount of all payments) – (initial loan)
Financial Accounting Intro Concepts Meth/Uses
14th Edition
ISBN:9781285595047
Author:Weil
Publisher:Weil
ChapterA: Appendix - Time Value Of Cash Flows: Compound Interest Concepts And Applications
Section: Chapter Questions
Problem 20E
Related questions
Question
A family has a $145,247, 15-years mortgage at 5.7 % compounded monthly.
(A) Find the monthly payment and the total interest paid. (equations on picture - equations for problem A)
Monthly payment: $____ (Round to two decimal places.)
Total interest paid: $____ (Round to two decimal places.)
(B) Suppose the family decides to add an extra $100 to its mortgage payment each month starting with the very first payment. How long will it take the family to pay off the mortgage? How much interest will the family save? (equations on picture - equations for problem B)
Time: ____ years (Round to two decimal places.)
Total interest paid: $____ (Round to two decimal places.)
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 5 steps with 4 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, finance and related others by exploring similar questions and additional content below.Recommended textbooks for you
Intermediate Accounting: Reporting And Analysis
Accounting
ISBN:
9781337788281
Author:
James M. Wahlen, Jefferson P. Jones, Donald Pagach
Publisher:
Cengage Learning
Intermediate Accounting: Reporting And Analysis
Accounting
ISBN:
9781337788281
Author:
James M. Wahlen, Jefferson P. Jones, Donald Pagach
Publisher:
Cengage Learning