The Following Table Lists Two Investment Plans, A And B. Determine Which Investment Is An Ordinary Annuity And The Future Value Of The Ordinary Annuity After One Year, Given That Both Investments, A And B, Compound Interest Monthly At The Rate Of

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The Power of Compounding: Determining Ordinary Annuities and Calculating Future Values

In the world of finance, understanding the concept of annuities and compound interest is crucial for making informed investment decisions. An annuity is a series of fixed payments made at equal intervals over a specified period of time. When these payments are made at the beginning of each period, it is called an ordinary annuity. In this article, we will explore two investment plans, A and B, and determine which one is an ordinary annuity. We will also calculate the future value of the ordinary annuity after one year, given that both investments compound interest monthly at the rate of 12%.

An annuity is a type of investment that provides a steady stream of income over a specified period of time. There are two main types of annuities: ordinary annuity and annuity due. An ordinary annuity is a series of fixed payments made at the end of each period, while an annuity due is a series of fixed payments made at the beginning of each period.

The following table lists two investment plans, A and B:

Investment Plan Payment Amount Number of Payments Interest Rate Compounding Frequency
A $100 12 12% Monthly
B $100 12 12% Monthly

To determine which investment is an ordinary annuity, we need to examine the payment schedule of each investment. In investment plan A, the payment amount is $100, and the payments are made at the end of each month. This means that the first payment is made at the end of the first month, the second payment is made at the end of the second month, and so on. In investment plan B, the payment amount is also $100, but the payments are made at the beginning of each month. This means that the first payment is made at the beginning of the first month, the second payment is made at the beginning of the second month, and so on.

Based on the payment schedules, we can conclude that investment plan B is an ordinary annuity, while investment plan A is an annuity due.

To calculate the future value of the ordinary annuity, we can use the formula for the future value of an annuity:

FV = PMT x [(1 + r/n)^(n*t) - 1] / (r/n)

Where:

  • FV = future value
  • PMT = payment amount
  • r = interest rate
  • n = compounding frequency
  • t = number of periods

In this case, the payment amount (PMT) is $100, the interest rate (r) is 12%, the compounding frequency (n) is 12 (monthly), and the number of periods (t) is 12 (one year).

Plugging in the values, we get:

FV = $100 x [(1 + 0.12/12)^(12*12) - 1] / (0.12/12) FV = $100 x [(1 + 0.01)^12 - 1] / 0.01 FV = $100 x [(1.01)^12 - 1] / 0.01 FV = $100 x (1.12683 - 1) / 0.01 FV = $100 x 0.12683 / 0.01 FV = $100 x 12.683 FV = $1268.30

Therefore, the future value of the ordinary annuity after one year is $1268.30.

In conclusion, investment plan B is an ordinary annuity, while investment plan A is an annuity due. We calculated the future value of the ordinary annuity after one year using the formula for the future value of an annuity. The result shows that the future value of the ordinary annuity is $1268.30.

  • "Annuity" by Investopedia
  • "Compound Interest" by Investopedia
  • "Future Value of an Annuity" by Calculator.net
  • Q: What is an ordinary annuity? A: An ordinary annuity is a series of fixed payments made at the end of each period.
  • Q: What is an annuity due? A: An annuity due is a series of fixed payments made at the beginning of each period.
  • Q: How do I calculate the future value of an ordinary annuity? A: You can use the formula for the future value of an annuity: FV = PMT x [(1 + r/n)^(n*t) - 1] / (r/n)
  • Annuity: A series of fixed payments made at equal intervals over a specified period of time.
  • Ordinary Annuity: A series of fixed payments made at the end of each period.
  • Annuity Due: A series of fixed payments made at the beginning of each period.
  • Compound Interest: The interest earned on both the principal amount and any accrued interest over a specified period of time.
  • Future Value: The total amount of money that an investment will be worth after a specified period of time.
    Frequently Asked Questions: Annuities and Compound Interest =============================================================

Q: What is an annuity?

A: An annuity is a series of fixed payments made at equal intervals over a specified period of time. It can be used to provide a steady stream of income, such as a pension or a retirement account.

Q: What is the difference between an ordinary annuity and an annuity due?

A: An ordinary annuity is a series of fixed payments made at the end of each period, while an annuity due is a series of fixed payments made at the beginning of each period.

Q: How do I calculate the future value of an annuity?

A: You can use the formula for the future value of an annuity: FV = PMT x [(1 + r/n)^(n*t) - 1] / (r/n), where:

  • FV = future value
  • PMT = payment amount
  • r = interest rate
  • n = compounding frequency
  • t = number of periods

Q: What is compound interest?

A: Compound interest is the interest earned on both the principal amount and any accrued interest over a specified period of time. It is calculated by multiplying the principal amount by the interest rate and then adding the interest to the principal amount.

Q: How does compound interest work?

A: Compound interest works by earning interest on both the principal amount and any accrued interest. For example, if you deposit $100 into a savings account with a 10% annual interest rate, you will earn $10 in interest in the first year. In the second year, you will earn interest on both the principal amount ($100) and the accrued interest ($10), resulting in a total interest of $11.

Q: What is the formula for compound interest?

A: The formula for compound interest is A = P x (1 + r/n)^(n*t), where:

  • A = final amount
  • P = principal amount
  • r = interest rate
  • n = compounding frequency
  • t = number of periods

Q: How often is interest compounded?

A: Interest can be compounded daily, monthly, quarterly, or annually, depending on the type of account and the financial institution.

Q: What is the difference between simple interest and compound interest?

A: Simple interest is calculated by multiplying the principal amount by the interest rate and then adding the interest to the principal amount. Compound interest, on the other hand, earns interest on both the principal amount and any accrued interest.

Q: How do I calculate the future value of a single payment?

A: You can use the formula for the future value of a single payment: FV = PV x (1 + r/n)^(n*t), where:

  • FV = future value
  • PV = present value
  • r = interest rate
  • n = compounding frequency
  • t = number of periods

Q: What is the formula for the present value of an annuity?

A: The formula for the present value of an annuity is PV = PMT x [(1 - (1 + r/n)^(n*t)) / (r/n)], where:

  • PV = present value
  • PMT = payment amount
  • r = interest rate
  • n = compounding frequency
  • t = number of periods

Q: How do I calculate the present value of a single payment?

A: You can use the formula for the present value of a single payment: PV = FV / (1 + r/n)^(n*t), where:

  • PV = present value
  • FV = future value
  • r = interest rate
  • n = compounding frequency
  • t = number of periods

Q: What is the difference between a fixed rate and a variable rate?

A: A fixed rate is a rate that remains the same over a specified period of time, while a variable rate is a rate that can change over time.

Q: How do I calculate the interest rate on a loan?

A: You can use the formula for the interest rate on a loan: r = (PMT / PV) x (1 / (1 - (1 + r/n)^(n*t))), where:

  • r = interest rate
  • PMT = payment amount
  • PV = present value
  • n = compounding frequency
  • t = number of periods

Q: What is the formula for the total amount paid on a loan?

A: The formula for the total amount paid on a loan is TP = PV + (PV x r), where:

  • TP = total amount paid
  • PV = present value
  • r = interest rate

Q: How do I calculate the total amount paid on a loan?

A: You can use the formula for the total amount paid on a loan: TP = PV + (PV x r), where:

  • TP = total amount paid
  • PV = present value
  • r = interest rate

Q: What is the difference between a loan and an investment?

A: A loan is a type of debt that requires repayment, while an investment is a type of asset that can generate income.

Q: How do I calculate the return on investment (ROI) on an investment?

A: You can use the formula for the ROI on an investment: ROI = (Gain / Cost) x 100, where:

  • ROI = return on investment
  • Gain = profit
  • Cost = initial investment

Q: What is the formula for the internal rate of return (IRR) on an investment?

A: The formula for the IRR on an investment is IRR = (1 + r/n)^(n*t) - 1, where:

  • IRR = internal rate of return
  • r = interest rate
  • n = compounding frequency
  • t = number of periods

Q: How do I calculate the internal rate of return (IRR) on an investment?

A: You can use the formula for the IRR on an investment: IRR = (1 + r/n)^(n*t) - 1, where:

  • IRR = internal rate of return
  • r = interest rate
  • n = compounding frequency
  • t = number of periods

Q: What is the difference between a bond and a stock?

A: A bond is a type of debt that requires repayment, while a stock is a type of equity that represents ownership in a company.

Q: How do I calculate the yield on a bond?

A: You can use the formula for the yield on a bond: Yield = (Coupon / Face Value) x 100, where:

  • Yield = yield on bond
  • Coupon = interest payment
  • Face Value = principal amount

Q: What is the formula for the yield to maturity (YTM) on a bond?

A: The formula for the YTM on a bond is YTM = (1 + r/n)^(n*t) - 1, where:

  • YTM = yield to maturity
  • r = interest rate
  • n = compounding frequency
  • t = number of periods

Q: How do I calculate the yield to maturity (YTM) on a bond?

A: You can use the formula for the YTM on a bond: YTM = (1 + r/n)^(n*t) - 1, where:

  • YTM = yield to maturity
  • r = interest rate
  • n = compounding frequency
  • t = number of periods

Q: What is the difference between a mutual fund and an exchange-traded fund (ETF)?

A: A mutual fund is a type of investment that pools money from multiple investors to invest in a variety of assets, while an ETF is a type of investment that tracks a specific index or asset.

Q: How do I calculate the return on investment (ROI) on a mutual fund or ETF?

A: You can use the formula for the ROI on a mutual fund or ETF: ROI = (Gain / Cost) x 100, where:

  • ROI = return on investment
  • Gain = profit
  • Cost = initial investment

Q: What is the formula for the internal rate of return (IRR) on a mutual fund or ETF?

A: The formula for the IRR on a mutual fund or ETF is IRR = (1 + r/n)^(n*t) - 1, where:

  • IRR = internal rate of return
  • r = interest rate
  • n = compounding frequency
  • t = number of periods

Q: How do I calculate the internal rate of return (IRR) on a mutual fund or ETF?

A: You can use the formula for the IRR on a mutual fund or ETF: IRR = (1 + r/n)^(n*t) - 1, where:

  • IRR = internal rate of return
  • r = interest rate
  • n = compounding frequency
  • t = number of periods

Q: What is the difference between a Roth IRA and a traditional IRA?

A: A Roth IRA is a type of retirement account that allows you to contribute after-tax dollars and withdraw tax-free in retirement, while a traditional IRA is a type of retirement account that allows you to contribute pre-tax dollars and withdraw taxable in retirement.

**Q: How do I calculate the return on investment (