Engineering Mathematics for Computerized Licensure Exam

Compounded quarterly

Interest calculated on the initial principal and also on the accumulated interest from previous periods, with compounding occurring four times a year.

Promissory note

A written promise to pay a specified amount of money to a specified person at a specified time.

Net interest

The amount of interest received after taxes or other deductions.

Principal amount

The original sum of money borrowed or invested, excluding any interest or fees.

Discount rate

The interest rate used to determine the present value of future cash flows.

Time value of money

The concept that money available now is worth more than the same amount in the future due to its potential earning capacity.

Future value

The value of a current asset at a specified date in the future based on an assumed rate of growth.

Investment return

The gain or loss made on an investment relative to the amount invested.

Annual percentage rate (APR)

The annual rate charged for borrowing or earned through an investment, expressed as a percentage.

Effective interest rate

The interest rate that reflects the true cost of borrowing, taking into account the amount received and the total amount to be paid back.

Simple interest rate

The percentage of the principal amount that is paid as interest over a specified period.

Banker's Discount

The interest deducted in advance from a loan amount, which is based on the total amount due.

Nominal interest rate

The stated interest rate before taking inflation or compounding into account.

Withholding tax

A percentage of interest that is deducted from the total interest earned before it is paid out.

Discounted loan

A loan where the interest is deducted from the principal before the borrower receives the funds.

Present worth

The current value of a future sum of money given a specified rate of return.

Effective rate

The actual interest rate earned or paid on an investment or loan, taking into account the effects of compounding.

Simple discount

A reduction in the amount due based on the interest rate and time until payment.

Compound interest

Interest calculated on the initial principal and also on the accumulated interest of previous periods.

Loan amount

The total sum of money that is borrowed from a lender.

Loan term

The duration over which a loan is to be repaid.

Interest calculation

The process of determining the amount of interest owed on a loan or earned on an investment.

Loan amortization

The process of paying off a debt over time through regular payments.

Investment horizon

The total length of time that an investor expects to hold a security or a portfolio.

Cash flow

The total amount of money being transferred into and out of a business, especially as it relates to liquidity.

Financial leverage

The use of borrowed funds to increase the potential return on investment.

Risk premium

The return in excess of the risk-free rate of return that investors require as compensation for the risk of an investment.

Yield

The income return on an investment, typically expressed as a percentage.

Time to triple money

21.97 years at 5% per annum compounded continuously.

Investment for P40,000

P24,751.34 at 6% compounded continuously for 8 years.

Equivalent nominal annual interest

3.92% for an effective annual interest rate of 4%.

Nominal rate of interest for 10 years

3% if the compound amount factor is equal to 1.34986.

Effective rate of interest

19.72% charged by American Express Corp. for 1.5% interest per month compounded continuously.

Effective annual rate from nominal interest

12.75% if the nominal interest is 12% compounded continuously.

Difference in future amount

P3.87 between P500 compounded annually at 5% and compounded continuously for 5 years.

Nominal rate for continuously compounded loan

21.51% if the effective rate is 24%.

Nominal rate for 8 years

4% if the present worth factor is equal to 0.6187835.

Difference between simple and compound interest

P155 for P5000 accumulated at 10% simple interest and 10% compound interest per year.

Discount on P2,000

P76.92 if discounted for 6 months at 8% compounded quarterly.

Single payment present worth factor

0.333 if a sum of money triples at a given rate of interest.

Interest rate from single payment amount factor

8% if the factor for 5 years is 1.33822.

Interest rate from single payment present worth factor

6% if the factor for 8 years is equal to 0.58201.

Single payment amount factor

1.60844 for 8% compounded quarterly over 6 years.

Withdrawn amount after 16 years

P507.42 if P1,000 is invested at an effective annual interest of 5%.

Interest on P200,000 at simple interest

P274,000 at a rate of 16% over 8 years.

Interest on P200,000 at compounded bi-monthly

P507,267.28 at 16% over 8 years.

Interest on P200,000 at compounded continuously

P422,462.64 at 16% over 8 years.

Value of x in (F/P, x, 6)

7% if F/P compounded quarterly is equal to 1.612226.

Value of y in (P/F, 6%, y)

7 years if P/F compounded bi-monthly is equal to 0.787566.

Rate of interest from compound amount factor

7% if compounded bi-monthly for 5 years equals 1.487887.

Nominal rate for effective rate of 8.33%

7% if compounded continuously.

Equivalent compound amount factor

1.61607 if compounded continuously.

Equivalent present worth factor

1.249347 if compounded continuously.

Time for loan to equal P3280

7 years at 8% simple interest.

Time for loan at 8% compounded quarterly

6.25 years.

Time for loan at 8% compounded continuously

7.18 years.

Nominal rate of interest for P1000 to P1608.44

12% if compounded bi-monthly over 4 years.

Effective rate for nominal interest of 8%

8.33% if compounded continuously.

Compound amount factor (compounded continuously)

1.377128

Present worth factor (compounded continuously)

1.272441

Single payment amount factor for 5 years

1.33822

Nominal rate of interest for single payment amount factor

6.00%

Effective rate of interest (semi-annually) for problem# 74

6.92%

Equivalent nominal rate (quarterly) for problem# 74

6.12%

Rate of interest (compounded quarterly) to quadruple in 17.5 years

6.23%

Actual interest rate for problem# 77

7.24%

Equivalent rate (daily) for problem# 77

7.24%

Total payment at the end of 5 years (12% simple interest)

P800,000.00

Total payment at the end of 5 years (12% compound semi-quarterly)

P911,059.20

Total payment at the end of 5 years (12% compound continuously)

P911,059.20

Interest earned on P60,000 at 6% compounded quarterly for 9 years and 3 months

P43,214.24

Years to earn P50,000 on P100,000 at 9% compounded quarterly

4.56 years

Rate of interest (compounded quarterly) for P200,000 to earn P120,000 in 5 years

9.5%

Lowest effective rate of interest

11.6% compounded monthly

Years to quadruple money at 7% compounded semi-annually

20.15 years

Years to treble money at x% compounded quarterly

13.87 years

Interest rate for P1,000 to grow to P2,370 in 15 years (semi-annually)

4.9%

Comparison of borrowing P3,500 at different interest rates

save P55 by borrowing from your friend

Present worth of P1,000,000 in 10 years at 12% compounded quarterly

P30,444.44

Net value of P80,000 deposit after three quarters at 6% compounded monthly

P95,324.95

Effective rate of interest for 14% compounded semi-annually

14.49%

Total amount after 5 years on P50,000 at 7.5% interest

P71,781.47

Effective rate corresponding to 18% compounded daily

19.39%

Nominal rate and effective rate for P1,000 becoming P1,126.49 in 4 years

4.29% and 4.32%

Conversion of 12% semi-annually to compounded quarterly

19.23%

Effective interest rate for 18% compounded semi-quarterly

19.25%

Compounded interest on P5,000 at 8% for 10 years

P6,005.30

Lump sum due after borrowing P4,000 for 6 years at 12%

P14,842.40

Future value of P200,000 at 24% compounded semi-annually after 5 years

P621,170

Compounded interest on P500,000 at 11.25% after 7 years and 9 months

P690,849

Years for P200,000 at 24% compounded semi-annually to reach P621,170

5 years

Compounding frequency for 9.5% accounts yielding 9.84% annually

monthly

Amount to accumulate for a car purchase with inflation and resale value appreciation

P120,289.51

Future value of P10,000 invested at 15% for 5 years with 6% inflation

P15,386.00

Total cost of a purchased and installed machine

P18,000.00

Machine Purchase Cost

A machine has been purchased and installed at a total cost of P18,000.00.

Scrap Value

The machine will be retired at the end of 5 years, at which time it is expected to have a scrap value of P2,000.00.

Inflation Rate

If an average annual rate of inflation of 3% is anticipated, how much capital must be accumulated?

Interest Rate for Inflation

If the inflation rate is 6%, cost of money is 10%, what interest rate will take care of inflation and the cost of money?

Government Bond

A man bought a government bond which cost P1000 and will pay P50 interest each year for 20 years.