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

Answer from: Quest

answer; im thinking customer:

Answer from: Quest

answer; ///i believe the correct answer is(e) complementary to each other;

Another question on Business

Business, 21.06.2019 19:20

Which of the following statements is true? a. financial investment refers to the creation and expansion of business enterprisesb. economic investment refers to the creation and expansion of business enterprisesc. economic investment refers to the purchase of assets such as stocks, bonds, and real estated. both economic and financial investment refer to the purchase of assets such as stocks, bonds, and real estate

Answers: 2

Answer

Business, 21.06.2019 20:30

Andrew cooper decides to become a part owner of a corporation. as a part owner, he expects to receive a profit as payment because he has assumed the risk of - serious inflation eroding the purchasing power of his investment.- being paid before the suppliers and employees are paid.- losing his home, car, and life savings.- losing the money he has invested in the corporation and not receiving profits.- the company giving all of the profits to local communities

Answers: 2

Answer

Business, 22.06.2019 09:40

You plan to invest some money in a bank account. which of the following banks provides you with the highest effective rate of interest? hint: perhaps this problem requires some calculations. bank 1; 6.1% with annual compounding. bank 2; 6.0% with monthly compounding. bank 3; 6.0% with annual compounding. bank 4; 6.0% with quarterly compounding. bank 5; 6.0% with daily (365-day) compounding.

Answers: 3

Answer

Business, 22.06.2019 14:30

What’s the present value of a perpetuity that pays $250 per year if the appropriate interest rate is 5%? $4,750 $5,000 $5,250 $5,513 $5,788what is the present value of the following cash flow stream at a rate of 8.0%, rounded to the nearest dollar? cash flows: today (t = 0) it is $750, after one year (t = 1) it is $2,450, at t = 2 it is $3,175, and at t=3 it is $4,400. draw a time line. $7,917 $8,333 $8,772 $9,233 $9,695

Answers: 2

Answer

You know the right answer?

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

Questions