General Mathematics - First Semester (2nd Quarter)
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Questions and Answers

Which of the following is the formula for calculating simple interest?

  • F = P + Is
  • F = P (1 + rt)
  • Is = Prt (correct)
  • F = P (1 + rt)

    • What is the interest earned if 1 million pesos is deposited in a savings account with a 0.25% annual simple interest rate for 1 year?

  • 2,000 pesos
  • 1,800 pesos
  • 2,030 pesos
  • 2,500 pesos (correct)

    • If you borrow 4,000 pesos and pay it after 6 months at an 8% simple annual interest rate, how much interest will you pay?

  • 160 pesos (correct)
  • 945 pesos
  • 1,800 pesos
  • 2,030 pesos

    • What is the balance after 18 months if 15,000 pesos is deposited into a savings account with a 4.2% simple annual interest rate?

    <p>15,945 pesos</p> Signup and view all the answers

    If a savings account earned an interest of 1,800 pesos at a 5% simple interest rate, for how long was the account deposited if the principal amount was 20,000 pesos?

    <p>1.8 years</p> Signup and view all the answers

    Which of the following is the formula for calculating simple interest?

    <p>Is = Prt</p> Signup and view all the answers

    What is the interest earned if 2,000 pesos is deposited in a savings account with a 2% annual simple interest rate for 1 year?

    <p>80 pesos</p> Signup and view all the answers

    How much interest will you pay if you borrow 5,000 pesos and pay it after 3 months at a 6% simple annual interest rate?

    <p>150 pesos</p> Signup and view all the answers

    Find the balance after 2 years if you put 10,000 pesos into a savings account that offers a 3.5% simple annual interest.

    <p>10,700 pesos</p> Signup and view all the answers

    Suppose you save 3,500 pesos of your allowance and deposit it in your account which earns simple annual interest. After 1 year, the balance is 3,605 pesos. Find the annual interest rate.

    <p>4%</p> Signup and view all the answers

    Which of the following is the correct formula for calculating simple interest?

    <p>Is = Prt</p> Signup and view all the answers

    What is the interest earned if 500,000 pesos is deposited in a savings account with a 0.5% annual simple interest rate for 2 years?

    <p>2,500 pesos</p> Signup and view all the answers

    If you borrow 10,000 pesos and pay it after 1 year at a 6% simple annual interest rate, how much interest will you pay?

    <p>1,000 pesos</p> Signup and view all the answers

    What is the balance after 2 years if 50,000 pesos is deposited into a savings account with a 3% simple annual interest rate?

    <p>52,000 pesos</p> Signup and view all the answers

    Suppose you save 5,000 pesos of your allowance and deposit it in your account which earns simple annual interest. After 6 months, the balance is 5,100 pesos. Find the annual interest rate.

    <p>2%</p> Signup and view all the answers

    Which formula is used to calculate the principal amount in compound interest?

    <p>$P = F(1+rm)^{-mt}$</p> Signup and view all the answers

    What is the principal amount in the given example?

    <p>$12,278.27</p> Signup and view all the answers

    What is the rate of compound interest in the given example?

    <p>12.33%</p> Signup and view all the answers

    What is the time period in the given example?

    <p>4.57 years</p> Signup and view all the answers

    Which formula is used to calculate the time period in compound interest?

    <p>$t = \log \left(\frac{F},{P}\right) / \log \left(1+rm\right)$</p> Signup and view all the answers

    Which formula is used to calculate the principal amount in compound interest?

    <p>$P = F(1+rm)^{mt}$</p> Signup and view all the answers

    Which formula is used to calculate the time period in compound interest?

    <p>$t = \log \left(\frac{F},{P}\right) / \log(1+rm)$</p> Signup and view all the answers

    What is the rate of compound interest in the given example?

    <p>0.1233 or 12.33%</p> Signup and view all the answers

    What must be the rate compounded quarterly for 8,000 pesos to accumulate to 10,200 pesos in 2 years?

    <p>0.1233 or 12.33%</p> Signup and view all the answers

    For how many years will 8,000 pesos accumulate to 10,000 if invested in a bank at 5% compounded annually?

    <p>4.57 years</p> Signup and view all the answers

    Which formula is used to calculate the principal amount in compound interest?

    <p>$F = P(1+rm)mt$</p> Signup and view all the answers

    What is the balance after 2 years if 50,000 pesos is deposited into a savings account with a 3% simple annual interest rate?

    <p>$51,500$</p> Signup and view all the answers

    Which formula is used to calculate the time period in compound interest?

    <p>$t = \log \frac{F},{P} \div \log (1+rm)$</p> Signup and view all the answers

    What is the interest earned if 1 million pesos is deposited in a savings account with a 0.25% annual simple interest rate for 1 year?

    <p>$2,500$</p> Signup and view all the answers

    What is the interest earned if 500,000 pesos is deposited in a savings account with a 0.5% annual simple interest rate for 2 years?

    <p>$2,500$</p> Signup and view all the answers

    Which formula is used to calculate the present value (principal) in compound interest?

    <p>P = F(1 + rm)mt</p> Signup and view all the answers

    What is the present value (principal) of an investment that will accumulate to 12,278.27 pesos at the end of 5 years, if the money was invested at 10% compounded semi-annually?

    <p>20,000 pesos</p> Signup and view all the answers

    What is the present value (principal) of an investment that will accumulate to 25,000 pesos at the end of 10 years, if the money was invested at 20% compounded annually?

    <p>25,000 pesos</p> Signup and view all the answers

    What is the present value (principal) of an investment that will accumulate to 27,600 pesos at the end of 8 years, if the money was invested at 30% compounded semi-annually?

    <p>12,000 pesos</p> Signup and view all the answers

    What is the present value (principal) of an investment that will accumulate to 36,000 pesos at the end of 6 years, if the money was invested at 10% compounded semi-annually?

    <p>36,000 pesos</p> Signup and view all the answers

    Which formula is used to calculate the present value (principal) in compound interest?

    <p>P = F(1+rm)^{mt}</p> Signup and view all the answers

    What is the present value (principal) of an investment that will accumulate to 12,278.27 pesos at the end of 5 years, if the money was invested at 10% compounded semi-annually?

    <p>$10,000</p> Signup and view all the answers

    What is the interest earned if 1 million pesos is deposited in a savings account with a 0.25% annual simple interest rate for 1 year?

    <p>$250</p> Signup and view all the answers

    What is the interest earned if 500,000 pesos is deposited in a savings account with a 0.5% annual simple interest rate for 2 years?

    <p>$5,000</p> Signup and view all the answers

    What is the rate of compound interest in the given example?

    <p>10%</p> Signup and view all the answers

    Which formula is used to calculate the present value (principal) in compound interest?

    <p>P = F(1 + rm)mt</p> Signup and view all the answers

    What is the principal amount in Example 1?

    <p>20,000 pesos</p> Signup and view all the answers

    What is the present value (principal) of an investment that will accumulate to 25,000 pesos at the end of 10 years, if the money was invested at 20% compounded annually?

    <p>20,000 pesos</p> Signup and view all the answers

    What is the rate of compound interest in Example 3?

    <p>30%</p> Signup and view all the answers

    What is the interest earned if 1 million pesos is deposited in a savings account with a 0.25% annual simple interest rate for 1 year?

    <p>2,500 pesos</p> Signup and view all the answers

    Which formula is used to calculate the nominal rate of compound interest?

    <p>r = m [FP1mt ─ 1]</p> Signup and view all the answers

    In Example 3, what must be the rate compounded semi-annually for 5,000 pesos to accumulate to 8,400 pesos in 7 years?

    <p>1.76%</p> Signup and view all the answers

    In Example 4, what must be the rate compounded monthly for 3,000 pesos to accumulate to 5,600 pesos in 8 years?

    <p>63.15%</p> Signup and view all the answers

    In Example 5, what must be the rate compounded quarterly for 9,000 pesos to accumulate to 12,800 pesos in 10 years?

    <p>85.78%</p> Signup and view all the answers

    What is the rate of compound interest in Example 1?

    <p>12.33%</p> Signup and view all the answers

    Which formula is used to calculate the nominal rate of compound interest?

    <p>r = m [FP1mt ─ 1]</p> Signup and view all the answers

    What is the rate of compound interest in Example 1?

    <p>12.33%</p> Signup and view all the answers

    What must be the rate compounded semi-annually for 5,000 pesos to accumulate to 8,400 pesos in 7 years?

    <p>1.76%</p> Signup and view all the answers

    What is the rate of compound interest in Example 3?

    <p>1.76%</p> Signup and view all the answers

    What is the principal amount in the given example?

    <p>8,000 pesos</p> Signup and view all the answers

    Which of the following is the correct formula for calculating the nominal rate of compound interest?

    <p>r = m [FP1mt ─ 1]</p> Signup and view all the answers

    What must be the rate compounded annually for 7,000 pesos to accumulate to 11,100 pesos in 5 years?

    <p>0.0966 or 9.66%</p> Signup and view all the answers

    What must be the rate compounded semi-annually for 5,000 pesos to accumulate to 8,400 pesos in 7 years?

    <p>1.76 or 1.76%</p> Signup and view all the answers

    What must be the rate compounded monthly for 3,000 pesos to accumulate to 5,600 pesos in 8 years?

    <p>0.6315 or 63.15%</p> Signup and view all the answers

    What must be the rate compounded quarterly for 9,000 pesos to accumulate to 12,800 pesos in 10 years?

    <p>0.8578 or 85.78%</p> Signup and view all the answers

    What is the rate of compound interest if 8,000 pesos accumulate to 10,200 pesos in 2 years, compounded quarterly?

    <p>0.1233%</p> Signup and view all the answers

    What is the rate of compound interest if 7,000 pesos accumulate to 11,100 pesos in 5 years, compounded annually?

    <p>0.0966%</p> Signup and view all the answers

    What is the rate of compound interest if 5,000 pesos accumulate to 8,400 pesos in 7 years, compounded semi-annually?

    <p>1.76%</p> Signup and view all the answers

    What is the rate of compound interest if 3,000 pesos accumulate to 5,600 pesos in 8 years, compounded monthly?

    <p>0.6315%</p> Signup and view all the answers

    What is the rate of compound interest if 9,000 pesos accumulate to 12,800 pesos in 10 years, compounded quarterly?

    <p>0.8578%</p> Signup and view all the answers

    What is the rate of compound interest if 3,000 pesos accumulate to 5,600 pesos in 8 years, compounded monthly?

    <p>0.6315%</p> Signup and view all the answers

    What is the rate of compound interest if 5,000 pesos accumulate to 8,400 pesos in 7 years, compounded semi-annually?

    <p>1.76%</p> Signup and view all the answers

    What is the rate of compound interest if 7,000 pesos accumulate to 11,100 pesos in 5 years, compounded annually?

    <p>0.0966%</p> Signup and view all the answers

    What is the rate of compound interest if 8,000 pesos accumulate to 10,200 pesos in 2 years, compounded quarterly?

    <p>0.1233%</p> Signup and view all the answers

    What is the rate of compound interest if 9,000 pesos accumulate to 12,800 pesos in 10 years, compounded quarterly?

    <p>85.78%</p> Signup and view all the answers

    Which formula is used to calculate the time period in compound interest?

    <p>t = log \left( \frac{F},{P} \right) \div m \log \left(1 + r \right)</p> Signup and view all the answers

    For how many years will 8,000 pesos accumulate to 10,000 if invested in a bank at 5% compounded annually?

    <p>4.5 years</p> Signup and view all the answers

    For how many years will 5,000 pesos accumulate to 15,300 if invested in a bank at 10% compounded semi-annually?

    <p>4.57 years</p> Signup and view all the answers

    For how many years will 8,000 pesos accumulate to 10,000 if invested in a bank at 5% compounded quarterly?

    <p>4.57 years</p> Signup and view all the answers

    For how many years will 8,000 pesos accumulate to 10,000 if invested in a bank at 5% compounded monthly?

    <p>4.57 years</p> Signup and view all the answers

    Which formula is used to calculate the time period in compound interest?

    <p>t = log(F/P) / (m * log(1 + r/m))</p> Signup and view all the answers

    What is the present value (principal) of an investment that will accumulate to 12,278.27 pesos at the end of 5 years, if the money was invested at 10% compounded semi-annually?

    <p>$10,000</p> Signup and view all the answers

    What is the interest earned if 500,000 pesos is deposited in a savings account with a 0.5% annual simple interest rate for 2 years?

    <p>$5,500</p> Signup and view all the answers

    What is the rate of compound interest if 7,000 pesos accumulate to 11,100 pesos in 5 years, compounded annually?

    <p>6%</p> Signup and view all the answers

    What is the principal amount in Example 1?

    <p>$8,000</p> Signup and view all the answers

    Which formula is used to calculate the time period in compound interest?

    <p>t = log(F/P) / (m * log(1 + r/m))</p> Signup and view all the answers

    Which formula is used to calculate the principal amount in compound interest?

    <p>P = F / (1 + r/m)^(m*t)</p> Signup and view all the answers

    What is the rate of compound interest in Example 1?

    <p>5%</p> Signup and view all the answers

    For how many years will 8,000 accumulate to 10,000 if invested in a bank at 5% compounded quarterly?

    <p>4 years</p> Signup and view all the answers

    What is the rate of compound interest if 5,000 accumulate to 8,400 in 7 years, compounded semi-annually?

    <p>8%</p> Signup and view all the answers

    Study Notes

    Simple Interest Calculations

    • Simple interest formula: ( I = P \times r \times t ), where ( I ) is interest, ( P ) is principal, ( r ) is rate (as a decimal), and ( t ) is time in years.
    • Interest earned from a 1 million pesos deposit at a 0.25% rate for 1 year:
      • Calculation: ( I = 1,000,000 \times 0.0025 \times 1 = 2,500 ) pesos.
    • Interest from borrowing 4,000 pesos at an 8% rate for 6 months:
      • Calculation: ( I = 4,000 \times 0.08 \times 0.5 = 160 ) pesos.
    • Balance after 18 months with a 15,000 pesos deposit at 4.2%:
      • Calculation: ( I = 15,000 \times 0.042 \times 1.5 = 945 ); Total balance = 15,000 + 945 = 15,945 pesos.
    • Duration of deposit for 1,800 pesos interest at 5% on a 20,000 pesos principal:
      • Rearrangement of the formula gives ( t = \frac{I}{P \times r} ); hence ( t = \frac{1,800}{20,000 \times 0.05} = 1.8 ) years or 1 year and 9 months.
    • Interest earned from a 2,000 pesos deposit at a 2% rate for 1 year:
      • Calculation: ( I = 2,000 \times 0.02 \times 1 = 40 ) pesos.
    • Interest on a 5,000 pesos loan at 6% for 3 months:
      • Calculation: ( I = 5,000 \times 0.06 \times 0.25 = 75 ) pesos.
    • Balance from a 10,000 pesos deposit at 3.5% for 2 years:
      • Calculation: ( I = 10,000 \times 0.035 \times 2 = 700 ) pesos; Total balance = 10,700 pesos.
    • Finding the annual interest rate from a 3,500 pesos deposit yielding 3,605 pesos after 1 year:
      • Interest earned = 3,605 - 3,500 = 105 pesos; therefore, ( r = \frac{I}{P \times t} = \frac{105}{3,500 \times 1} = 0.03 ) or 3%.

    Compound Interest Formulas and Calculations

    • Present value formula in compound interest:
      • This usually involves the formula ( PV = FV / (1 + r)^n ), where ( FV ) is future value, ( r ) is rate per period, and ( n ) is number of periods.
    • To find how much an investment grows with specific rates and terms using compound interest calculations.
    • 8,000 pesos growth to 10,200 pesos in 2 years compounded quarterly requires finding the effective interest rate.

    Compounding and Accumulations

    • Rate to turn 5,000 pesos into 8,400 pesos in 7 years compounded semi-annually can be calculated via rearranging the compound interest formula to find ( r ).
    • Rate insight if 70,000 pesos turns into 11,100 pesos in 5 years with compounding effects.
    • Duration it takes for accumulating investments with specific principal amounts at given interest rates across varying compounding frequencies.

    Summary of Investments

    • Repeated calculations involve varying principal amounts and interest rates to provide interest earnings or final balances after set durations.
    • Relate understanding of simple vs. compound interest affecting long-term savings and loans: Simple interest is straightforward, but compound interest can massively impact the total return over time due to calculations based on accrued interest.

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