Business, 24.07.2019 17:30, genyjoannerubiera

Aloan is amortized over five years with monthly payments (i. e. end of month) at an annual nominal interest rate of 5% compounded monthly. the first payment is 500 and is to be paid one month from the date of the loan. each succeeding monthly payment will be 20 more than the prior payment. calculate the outstanding loan balance immediately after the 40th payment is made.

Answers: 1

Show answers

Answers

Given:
Amortizing period = 5 years
APR=5% per annum
interest rate, i = 0.05/12 per month
number of periods, n = 5*12=60 months (for amortization)
Payment schedule:
$500 at the end of first month,
increased by $20 each month thereafter.
Borrowed amount: not given

Question: Find outstanding loan balance after the 40th payment.

Solution:
Step 1: First we need to find the amount borrowed, P.
From the payment schedule, we decompose the payment into two components,

A. Equivalent uniform monthly payment, As, for a step amount of G=$20 a month, starting with zero after the first month, for a period of 5 years (n=60).
The value of As can be obtained from a specialized formula for step-payments,
$As=\frac{G((1+i)^{n}-i*n-1)}{i(1+i)^{n}-i}$
Substitute values, G=20,i=0.05/12,n=60
$As=\frac{20((1+.05/12)^{60}-(.05/12)*60-1)}{(.05/12)(1+.05/12)^{60}-(.05/60)}$
=565.0847

B. Principal, Pb, for a uniform monthly payment of A a month
The principal,Pb can be found from the basic amortizing formula to be
$Pb=\frac{A((1+i)^{n}-1)}{i(1+i)^{n}}$
We have
Equivalent uniform monthly payment
=500+equivalent uniform payment step amounts
=500+565.0847
=1065.0847
substituting values, A=1065.0847,i=.05/12,n=60
$=\frac{1065.0847((1+.05/12)^{60}-1)}{(.05/12)(1+.05/12)^{60}}$
=56439.591
check: average monthly payment = 1100
duration: 60 months
total amount paid = 60*1100=66000
average annual interest=((66000-56439)/56439-1)/5=3.3% (~ 5%/2) ok.

Amount borrowed, P=56439.591

Step 2: Future value of loan at the end of the 40th month.
This can be found by the compound interest formula
F=P(1+i)^n=56439.591(1+0.05/12)^40=66652.416

Step 3: Future value of payments
first we need to find the equivalent monthly payment of the step payments, using the same formula as in step 1, but with n=40
$A=\frac{G((1+i)^{n}-i*n-1)}{i(1+i)^{n}-i}$
$=\frac{20((1+0.05/12)^{40}-(0.05/12)*40-1)}{(0.05/12)(1+0.05/12)^{40}-(0.05/12)}$
=378.924
This should be added to the constant payment of $500 a month to give
A=500+378.924=878.924
Future value of monthly payment of 878.924
$F=\frac{A((1+i)^{n}-1)}{i}$
Substitute values, A=878.924, i=0.05/12, n=40
$=\frac{878.924((1+0.05/12)^{40}-1)}{0.05/12}$
=38170.213

Step 4: Outstanding balance right after the 40th payment
=future value of loan - future value of payments
=66652.416-38170.213
=28482.20

Outstanding balance after the 40th payment is $28482.20

answered: Guest

looks

answered: Guest

answer; according to the ( irs );

Other questions on the subject: Business

Business, 21.06.2019 18:10, diamondk2019

In a sumif conditional function, what should be the order of terms in the parentheses?

Answers: 1

continue

Business, 22.06.2019 01:50, mattstudy305

Which statement below best describes george waring's approach to solving the problems of water-borne illness? a. waring is going with his "gut," because he believes that instincts and emotions are the best guides for action. b. waring efficiently and thoroughly lays out the case for why the problems are too large and overwhelming to be solved: people should just move out of cities back to their farms. c. waring has gathered the testimonies of people who live in densely populated areas in order to learn how they themselves have solved their problems. d. waring exhibits the industrial age's increased respect for and reliance on science and the scientific method.

Answers: 1

continue

Business, 22.06.2019 05:00, jennemylesp19oy5

What is a sort of auction for stocks in which traders verbally submit their offers?

Answers: 3

continue

Business, 22.06.2019 19:30, smokey19

The usa today reports that the average expenditure on valentine's day is $100.89. do male and female consumers differ in the amounts they spend? the average expenditure in a sample survey of 47 male consumers was $135.67, and the average expenditure in a sample survey of 38 female consumers was $68.64. based on past surveys, the standard deviation for male consumers is assumed to be $34, and the standard deviation for female consumers is assumed to be $17.

Answers: 1

continue

Do you know the correct answer?

Aloan is amortized over five years with monthly payments (i. e. end of month) at an annual nominal i...