When you walk into a business and decide that you might want the job but then you really see what the people do and your like i
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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,
Substitute values, G=20,i=0.05/12,n=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
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
=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
=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
Substitute values, A=878.924, i=0.05/12, n=40
=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
Answer: Outstanding balance after the 40th payment is $28482.20
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,
Substitute values, G=20,i=0.05/12,n=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
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
=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
=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
Substitute values, A=878.924, i=0.05/12, n=40
=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
Answer: Outstanding balance after the 40th payment is $28482.20
Answer:
The Firm should not Buy and Install the press as it delivers a negative NPV of -$24,924 at 11% discount rate over its 4 year operations
Explanation:
The General rule is to appraise the investment based on various appraisal techniques.
A technique that should be considered must have special focus on the time value of money, the required rate of returns expected by the firm and other Cashflow considerations.
The Net Present Value (NPV) approach will be the best method to proceed with.
The NPV approach typically falls under the following decision tree:
a. If NPV is negative (Reject the proposal)
b. If NPV is positive (Accept if it's a singular project, Accept the highest positive NPV if it's for mutually exclusive Projects)
c. If Zero (this is the breakeven line at which the Project covers all its cost but does not return a profit.) Also referred to as the IRR
Kindly refer to the attached for detailed workings
