17 Questions
A man buys a house and lot worth Php 150,000 if paid in cash. On the installment basis, he pays Php 50,000 downpayment; Php 30,000 at the end of one year; Php 40,000 at the end of 2 years and a final payment at the end of 4 years. Find the final payment if interest is ______%
14
If money is worth 12% effective, what equal payments x at the end of 2 years and 4 years will equitably replace the obligations: Php 3,000 due in 3 years and Php 5,000 due in 5 years, both interest at ______% compounded annually
10
Find the accumulated amount after 5 years of Php 1,000 invested at a rate of ______% compounded continuously
10
An investment was made by an engineer in which he deposited Php 100,000.00 in a bank that offered 10% interest compounded monthly for 5 yrs and it will be 8% compounded continuously beyond 5 yrs, What will be the value of money at the end of ______ yrs
8
A man borrowed Php 2,000 from a bank and agreed to pay at the end of 6 months. The bank discounted the loan and gave him Php ______ cash.
1,920
If money is worth ______% effective, what equal payments x at the end of 2 years and 4 years will equitably replace the obligations: Php 3,000 due in 3 years and Php 5,000 due in 5 years, both interest at 10% compounded annually
12
On January 1 1998, Juan's father starts to fund with payments of Php 2,000 each during January 1 up to including Jan 1, 2007. At the 18th birthday, Php 3,000 shall be withdrawn for 5 years. The remaining fund is accumulated until Juan is 28 years old. If the fund earns 10%, how much will be paid to Juan in his 28th birthday? The topic is ____________.
accumulated amount
The purchaser of a tractor paid Php 10,000 cash and agreed to pay Php 3,000 at the end of each 6 months for 10 years. He failed to pay the first 5 payments. At the end of 3 years, the purchaser decided to pay a single payment which will cancel both his accumulated and future liabilities. What must he pay if money is worth 8% per annum compounded semiannually? The topic is ____________.
capital recovery factor
On January 1 1998, Juan's father starts to fund with payments of Php 2,000 each during January 1 up to including Jan 1, 2007. At the 18th birthday, Php 3,000 shall be withdrawn for 5 years. The remaining fund is accumulated until Juan is 28 years old. If the fund earns 10%, what factor should be used to calculate the present worth of the fund withdrawals at the 18th birthday? The topic is ____________.
present worth factor
The purchaser of a tractor paid Php 10,000 cash and agreed to pay Php 3,000 at the end of each 6 months for 10 years. He failed to pay the first 5 payments. At the end of 3 years, the purchaser decided to pay a single payment which will cancel both his accumulated and future liabilities. What is the term used to describe the process of calculating the single payment to cancel liabilities? The topic is ____________.
loan amortization
The purchaser of a tractor paid Php 10,000 cash and agreed to pay Php 3,000 at the end of each 6 months for 10 years. He failed to pay the first 5 payments. At the end of 3 years, the purchaser decided to pay a single payment which will cancel both his accumulated and future liabilities. If money is worth 8% per annum compounded semiannually, on what basis was the payment agreed upon? The topic is ____________.
installment basis
If, as an employee, she does not have to pay sales tax, how much more worth of merchandise (in terms of price before discount) will she be able to purchase by holding out to that day (nearest cent, if applicable)?ENGINEERING ECONOMICS 15 Compound Interest & Cash Flow ENGINEERING ECONOMICS 16 Compound Interest - In a compound interest, the interest is computed very end of each interest period, and the interest earned for that period is added to the principal.F= Future worth/ amount P= Principal Amount i= effective interest rate per period r= nominal rate of interest n= number of period m= mode of compounding t= no of years Effective Rate of Interest - Actual rate of interest on the principal for 1 year.ENGINEERING ECONOMICS 17 Mode of Compounding Annually or every 12 months Semi-annually or every 6 months Biannually or every two year Quarterly or every 3 months Semi-quarterly or every 1.5 months Monthly or every month Bimonthly or every 2 months Semi-monthly or every 0.5 months ENGINEERING ECONOMICS m=1 m=2 m=0.5 m=4 m=8 m=12 m=6 m=24 18 Sample Problem 1.Php 1M is invested with a nominal interest rate of 10% compounded quarterly, what is the final worth after a year?What is the effective rate of interest? 2.If P500,000 is invested at 8% interest compounded quarterly, how many years will it take for this amount to accumulate to P900,000?ENGINEERING ECONOMICS 19 Seatwork 1.
present worth factor
Write 6 ______ statements using the content above. Provide the missing word as the answer. Focus on topics: present worth factor, capital recovery factor, loan amortization, accumulated amount, installment basis. Write in English language.
fill in the blank
Php 1M is invested with a nominal interest rate of 10% compounded quarterly, what is the final worth after a year?What is the ______ rate of interest?
effective
If P500,000 is invested at 8% interest compounded quarterly, how many years will it take for this amount to accumulate to P900,000?
accumulated
______ basis
installment
Focus on topics: present worth factor, capital recovery factor, loan amortization, ______, installment basis.
accumulated amount
Study Notes
Engineering Economics
- A house and lot worth Php 150,000 can be paid in cash, or through an installment basis with a Php 50,000 downpayment, Php 30,000 at the end of 1 year, Php 40,000 at the end of 2 years, and a final payment at the end of 4 years, with an interest rate of 14%.
Equitable Replacement of Obligations
- Eq. Value Sample Problem 1: Find equal payments x at the end of 2 and 4 years that will replace obligations of Php 3,000 due in 3 years and Php 5,000 due in 5 years, both at 10% interest compounded annually, when money is worth 12% effective.
Continuous Compounding
- F = future worth, P = present worth, r = nominal rate, t = number of years
- Sample Problem 1: Find the accumulated amount after 5 years of Php 1,000 invested at 10% compounded continuously.
- Sample Problem 2: An investment of Php 100,000 at 10% interest compounded monthly for 5 years and 8% compounded continuously beyond 5 years, what is the value of money at the end of 8 years?
Discount, Future Worth, and Present Worth
- d = rate of discount, i = rate of interest
- Sample Problem 1: A man borrowed Php 2,000 and agreed to pay at the end of 6 months; the bank gave him Php 1,920 cash.
Annuities
- Sample Problem 5: The purchaser of a tractor paid Php 10,000 cash and agreed to pay Php 3,000 at the end of each 6 months for 10 years, but failed to pay the first 5 payments; what single payment must he pay to cancel both his accumulated and future liabilities, with money worth 8% per annum compounded semi-annually?
Compound Interest and Cash Flow
- Compound interest is computed at the end of each interest period, and the interest earned is added to the principal.
- Effective rate of interest is the actual rate of interest on the principal for 1 year.
Mode of Compounding
- Mode of compounding can be annually, semi-annually, biannually, quarterly, semi-quarterly, monthly, bimonthly, or semi-monthly.
Sample Problems
- Sample Problem 1: Php 1M is invested with a nominal interest rate of 10% compounded quarterly, what is the final worth after a year, and what is the effective rate of interest?
- Sample Problem 2: If P500,000 is invested at 8% interest compounded quarterly, how many years will it take for this amount to accumulate to P900,000?
Practice solving engineering economics problems involving house purchases, installment payments, interest rates, and equal payments. Calculate final payments and equal payments to replace obligations in different time frames.
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