Compound Interest Calculation Quiz
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Questions and Answers

What is the total amount in Esther's account at the end of four years?

  • ₱8,000
  • ₱8,161.51 (correct)
  • ₱8,350
  • ₱8,500

What is the formula used to calculate the compound amount A?

  • A = P(1 + r)^n
  • A = P(1 + r/n)^(nt) (correct)
  • A = P + Prt
  • A = P + I

How much interest does Esther earn on her investment?

  • ₱150
  • ₱180
  • ₱161.51 (correct)
  • ₱200

What is the present value (P) in the example for the 20-year investment?

<p>₱20,000 (C)</p> Signup and view all the answers

What is the principal amount in Esther's investment?

<p>₱8,000 (C)</p> Signup and view all the answers

What does the future value represent in an investment?

<p>The total value at a given interest rate (A)</p> Signup and view all the answers

If the interest rate is 0.5%, what is the corresponding decimal representation of this rate?

<p>0.005 (B)</p> Signup and view all the answers

How many total compounding periods are there in Esther's investment?

<p>16 (C)</p> Signup and view all the answers

How much total amount will be available after 20 years of investment of ₱20,000 at 4% interest compounded monthly?

<p>₱44,451.64 (C)</p> Signup and view all the answers

What is the maturity value of an investment?

<p>The amount it is worth in the future (D)</p> Signup and view all the answers

Which of the following correctly represents the formula for calculating the compound amount?

<p>A = P(1 + rac{r}{m})^{mn} (C)</p> Signup and view all the answers

What does the symbol 'I_C' represent in the context of compound interest?

<p>The compound interest earned (B)</p> Signup and view all the answers

What variables are used to calculate compound interest?

<p>Principal, time, and compounding frequency (A)</p> Signup and view all the answers

Which of the following is NOT a common value for the number of compounding periods in a year?

<p>10 for decennially (C)</p> Signup and view all the answers

What is the total amount in Esther's account after four years with quarterly compounding?

<p>₱8,323.12 (B)</p> Signup and view all the answers

What is the definition of compound interest?

<p>Interest added to the principal for future calculations (C)</p> Signup and view all the answers

What is the formula for calculating simple interest?

<p>𝐼 = 𝑃𝑟𝑡 (C)</p> Signup and view all the answers

If you invested ₱15,000 at a simple interest rate of 5% for 4 years, what is the interest earned?

<p>₱6,000 (C)</p> Signup and view all the answers

What value of 't' in the interest formula represents if the period is expressed in years?

<p>The fraction of a year invested (C)</p> Signup and view all the answers

What does the future value formula indicate about the relationship between investment amount and interest rate?

<p>Higher interest rates increase future value. (D)</p> Signup and view all the answers

In the context of finance, what does the variable 𝐹 represent?

<p>The future value of an investment. (C)</p> Signup and view all the answers

If the principal amount is ₱20,000 and the total interest earned in 2 years is ₱1,200, what is the interest rate?

<p>3% (D)</p> Signup and view all the answers

What is the purpose of the formula for present value?

<p>To determine the amount to invest today for a future target. (D)</p> Signup and view all the answers

What is the formula to calculate maturity value (MMM)?

<p>MMM = P(1 + r) (B)</p> Signup and view all the answers

How would you express 9 months in years for interest calculations?

<p>0.75 years (B)</p> Signup and view all the answers

If you want to accumulate ₱2,000,000 in 45 years at a 3% interest rate compounded quarterly, what is the calculated present value?

<p>₱521,098.87 (C)</p> Signup and view all the answers

If the principal (P) is ₱40,000 and the interest (I) is ₱9,600, what is the maturity value (MMM)?

<p>₱49,600 (D)</p> Signup and view all the answers

If a total simple interest of ₱4,500 is earned over a period of 3 years, with a principal of ₱15,000, what is the rate of interest?

<p>7.5% (A)</p> Signup and view all the answers

Given a principal of ₱32,000, an interest rate of 8%, and a time period of 180 days, what is the maturity value (MMM)?

<p>₱33,280 (D)</p> Signup and view all the answers

What does the variable 𝑚 represent in the formulas provided?

<p>The total number of compounding periods per year. (D)</p> Signup and view all the answers

In the context of simple interest, what does 'P' represent?

<p>The principal amount invested (C)</p> Signup and view all the answers

If you borrow ₱25,000 and pay ₱2,500 in interest over 1 year, what is the effective rate of interest?

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

How do you calculate the interest (I) using the principal (P) and the rate (r)?

<p>I = Prt (C)</p> Signup and view all the answers

What would be the future value of ₱15,000 compounded semi-annually for five years at 6% interest?

<p>₱20,158.75 (C)</p> Signup and view all the answers

When calculating present value, what does the term 𝑛 represent?

<p>The total number of compounding periods over the investment duration. (A)</p> Signup and view all the answers

What is the value of I when the principal is ₱37,500, the rate is 8%, and the time is 146 days?

<p>₱1,200 (C)</p> Signup and view all the answers

What does the term 'maturity value' refer to in finance?

<p>The total amount owed after interest is added (D)</p> Signup and view all the answers

What happens to the present value if the interest rate increases while keeping the future value constant?

<p>The present value decreases. (D)</p> Signup and view all the answers

Which statement correctly describes the relationship between interest and principal?

<p>Interest is derived from the principal multiplied by the rate and time. (D)</p> Signup and view all the answers

What is the correct value of the principal (P) if the interest earned (Ie) is ₱1,200 at an 8% rate for 146 days?

<p>₱37,500 (B)</p> Signup and view all the answers

How much must be invested today to reach ₱2,000,000 in 45 years?

<p>₱521,098.87 (C)</p> Signup and view all the answers

If the interest rate (r) is unknown, which formula should be used?

<p>$r = m imes (F/P - 1)$ (C)</p> Signup and view all the answers

When the number of compounding periods (m) is unknown, which expression is used?

<p>$m = rac{n}{F/P}$ (B)</p> Signup and view all the answers

What is the formula to find the total number of compounding periods (n) when unknown?

<p>$n = rac{F}{P imes r}$ (D)</p> Signup and view all the answers

When time is unknown, how can total compounding periods (n) be expressed?

<p>$t = rac{n}{m}$ (B)</p> Signup and view all the answers

What does the variable F represent in future value calculations?

<p>Future value amount (C)</p> Signup and view all the answers

In the context of compounding, which of the following factors is NOT a variable needed to calculate future value?

<p>Market volatility (v) (A)</p> Signup and view all the answers

If you want to calculate future value, which of the following formulas must NOT include the logarithm?

<p>$F = P(1 + r)^n$ (D)</p> Signup and view all the answers

Flashcards

Principal (P)

The amount of money borrowed or invested.

Interest (I)

The interest earned over a specific time period.

Interest Rate (r)

The percentage rate at which interest accumulates.

Time (t)

The time for which interest is calculated.

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Maturity Value (M)

The total amount of money owed or received at the end of a loan or investment period.

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Simple Interest Formula

The formula used to calculate the total interest earned or paid.

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Simple Interest

Interest calculated only on the principal amount.

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Compound Interest

A type of interest calculation where interest is added to the principal and then earns interest itself.

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Compound Amount (A)

The total amount of money accumulated after a certain period, including both the principal and the interest earned.

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Compounding Frequency (m)

The number of times interest is compounded each year.

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Number of Compounding Periods (n)

The total number of compounding periods.

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Compound Interest (IC)

The difference between the compound amount (A) and the principal (P). It represents the total interest earned throughout the investment period.

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Future Value (FV)

The amount that matured from the principal, representing its worth in the future.

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Present Value (PV)

The initial amount invested or borrowed, also known as the present value.

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Rate (r)

The fixed percentage rate applied to the principal each year.

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When Principal (P) is unknown

The principal is unknown.

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When Rate (r) is unknown

The rate is unknown.

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What is Future Value?

The future value (FV) of an investment is the amount of money it will grow to after a certain period at a certain rate of interest.

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What is 'r'?

The interest rate for a period.

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What is 'm'?

The number of times interest is compounded per year.

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What is 'n'?

The number of compounding periods.

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What is the formula for calculating Future Value?

The formula to calculate the future value (FV) of an investment.

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What is Present Value?

The present value (PV) of an investment is the amount of money you need to invest today to achieve a target amount in the future.

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What is the formula for calculating Present Value?

The formula to calculate the present value (PV) of an investment.

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What is the process of calculating Future Value?

The process of calculating the future value of an investment involves determining the amount of money it will grow to after a certain period at a certain rate of interest, considering compounding.

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Annual Rate (r)

The annual interest rate, expressed as a decimal.

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Total Number of Compounding Periods (n)

The total number of compounding periods over the entire investment period.

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Compound Interest Formula

Formula for calculating the compound amount (A) based on principal (P), annual rate (r), number of compounding periods in a year (m), and total number of compounding periods (n).

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Present Value

The amount of money you need to invest today to reach a specific future value after a certain period.

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Future Value

The value your investment will grow to in the future, given a specific interest rate and time.

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Number of Compounding Periods in a Year (m)

The number of times interest is calculated and added to the principal in a year.

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Present Value Formula

The formula used to calculate the present value of an investment.

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Future Value Formula

The formula used to calculate the future value of an investment.

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Study Notes

Simple Interest

  • Simple interest is a fixed percentage of the total invested amount paid yearly.
  • Formula: I = Prt, where:
    • I = Simple interest
    • P = Principal (amount invested)
    • r = Interest rate (percentage)
    • t = Time (number of years)
  • Formulas for unknown variables:
    • P = I / rt
    • r = I / Pt
    • t = I / Pr

Example 1

  • Suppose P10,000 is deposited with a 10% simple interest rate for 3 years.
  • Calculate the interest earned: I = P10,000 * 0.10 * 3 = P3,000

Example 2

  • Cyndi borrowed P30,000.
  • The interest paid was P3,375 over 9 months.
  • Calculate the interest rate: r = 0.15 (using appropriate formula) or 15%.

Ordinary Interest

  • Ordinary interest calculates simple interest based on a 360-day year.

Example 3

  • Miss Uy borrowed P80,000.
  • The loan earned P5,400 at 9% ordinary interest.
  • Calculate the number of days it took to repay: t= 270 days

Exact Interest

  • Exact interest calculates simple interest based on a 365-day year.

Example 4

  • Mr. Sandoval paid P1,200 exact interest at 8% for 146 days.
  • Calculate the principal: P = P37,500

Compound Interest

  • Interest due is added to the previous balance, becoming the new principal for the next period.
  • Compound interest (Ic): Interest added to the principal.
  • Compound amount (A): Total amount at the end of the last period.
  • Formula: A = P(1 + r/m)^ (mn) where:
    • P = Principal (present value)
    • r = Annual interest rate
    • m = Number of compounding periods per year
    • n= Total number of compounding periods

Example 5

  • Esther deposited P8,000 in a savings account.
  • Compounded quarterly at 0.5% for four (4) years.
  • Compound amount: A = P8,161.51
  • Compound interest: Ic= P161.51

Example 6

  • How much interest is earned after 20 years by P20,000 at 4% interest compounded monthly.
  • Compound amount: A = P44,451.64
  • Compound interest: Ic= P24,451.64

Maturity Value

  • The final amount of an investment or debt with added interest.
  • Formula: MV = P(1+rt)

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Description

Test your understanding of compound interest with this quiz. Answer questions regarding formulas, principal amounts, interest rates, and investment growth over time. Perfect for finance enthusiasts or anyone looking to sharpen their investment knowledge.

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