Compound Interest Calculation
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Questions and Answers

What is the future value of £1000 invested at 0.12 for 6 years?

  • £1973.8 (correct)
  • £2263.8
  • £1513.8
  • £2503.8

    • What is the total interest earned in the second period?

  • £134.4 (correct)
  • £144.4
  • £154.4
  • £120

    • What is the present value of £2000 in 5 years' time at an interest rate of 11%?

  • £1186.9 (correct)
  • £1600
  • £1800
  • £1400

    • If you invest £1000 at 10% per year for 10 years, what is the future value?

    <p>£2593.7</p> Signup and view all the answers

    What is the difference between compound interest and simple interest?

    <p>Compound interest applies to both principal and interest, while simple interest applies to the original principal.</p> Signup and view all the answers

    If £1000 is invested at 20% per year for 5 years, what is the future value?

    <p>£1488.0</p> Signup and view all the answers

    What is the present value of £2000 in one year's time at 11%?

    <p>£1801.8</p> Signup and view all the answers

    How much do we need to invest now at 11% to give £2000 after one year?

    <p>£1801.8</p> Signup and view all the answers

    If you want to find the value of r, which formula would you use?

    <p>r = (FV/PV)^(1/t) - 1</p> Signup and view all the answers

    What is the value of t in the equation FV = PV (1 + r)^t, given FV = 2, PV = 1, and r = 14.87%?

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

    What is the PV of a series of cash flows of £2500, £900, and £3600 at the end of year 1, 4, and 6, respectively, at a rate of 9%?

    <p>5077.7</p> Signup and view all the answers

    What is the formula for the PV of an annuity of C at the end of each of the next t years at r per year?

    <p>PV = C x 1 - {1/(1+r)^t} / r</p> Signup and view all the answers

    What is the PV of a six-year annuity of £4000 at r = 8%?

    <p>£18,491.5</p> Signup and view all the answers

    What is the FV of a series of cash flows of £2500, £900, and £3600 at the end of year 1, 4, and 6, respectively, at a rate of 9% after 7 years?

    <p>9282.3</p> Signup and view all the answers

    What is the interest rate if your investment doubles in 5 years?

    <p>14.87%</p> Signup and view all the answers

    What is the purpose of the formula r = (FV/PV)^(1/t) - 1?

    <p>To find the interest rate of an investment</p> Signup and view all the answers

    What is the present value of £25,000 in 3½ years, assuming an interest rate of 12.5%?

    <p>16554.1</p> Signup and view all the answers

    What is the annual percentage rate (APR) that is equivalent to an effective annual rate (EAR) of 16%?

    <p>16%</p> Signup and view all the answers

    If you borrow £100 and make no repayments, how much would you owe after 3 years at an APR of 4200%?

    <p>7,500,000</p> Signup and view all the answers

    What is the future value of an investment of £100 after 3 years, with interest rates of 11%, 9%, and 13% in years 1, 2, and 3, respectively?

    <p>136.72</p> Signup and view all the answers

    What is the present value of £100 in 4 years' time, assuming interest rates of 8%, 12%, 6%, and 13% in years 1, 2, 3, and 4, respectively?

    <p>69.02</p> Signup and view all the answers

    What is the real return on an investment if you invest £100 for a year at 10% interest, and inflation is 7%?

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

    What is the nominal interest rate that is equivalent to a real interest rate of 3% and an inflation rate of 7%?

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

    If you invest £100 for a year at 10% interest, and inflation is 7%, how much can you buy at the end of the year?

    <p>107 copies of a newspaper</p> Signup and view all the answers

    What is the process of calculating the present value?

    <p>Discounting</p> Signup and view all the answers

    What is the relationship between real rate and nominal rate?

    <p>Real rate = Nominal rate - Inflation rate</p> Signup and view all the answers

    What is the formula for calculating the future value?

    <p>FV = PV (1 + r)t</p> Signup and view all the answers

    What happens to the effective interest rate when the compounding frequency increases?

    <p>It increases</p> Signup and view all the answers

    What is an annuity?

    <p>A series of payments</p> Signup and view all the answers

    What is the real cash payoff if the nominal cash payoff is £110 and the inflation rate is 7%?

    <p>£102.8</p> Signup and view all the answers

    What is the process of calculating the future value?

    <p>Compounding</p> Signup and view all the answers

    What is the difference between the nominal interest rate and the real interest rate?

    <p>The inflation rate</p> Signup and view all the answers

    What is the formula for the present value of a perpetuity?

    <p>PV = C / r</p> Signup and view all the answers

    What is the effective annual rate for a flat rate of 10% with semiannual compounding?

    <p>10.25%</p> Signup and view all the answers

    What is the interest earned on a £100 investment at a flat rate of 10% for 1 year, compounded monthly?

    <p>£10.47</p> Signup and view all the answers

    What is the formula for the future value of an investment with compounding?

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

    What is the present value of a cash flow stream of £30,000 per year, discounted at 12% for 10 years?

    <p>£5,309.5</p> Signup and view all the answers

    What is the formula to find the flat rate of interest given the effective annual rate?

    <p>r = m * [(1 + EAR)^(1/m) - 1]</p> Signup and view all the answers

    What is the advantage of using effective annual rates?

    <p>They are used for discounting and compounding for periods other than multiples of a year.</p> Signup and view all the answers

    What is the annuity where the cash flows continue forever?

    <p>Perpetuity</p> Signup and view all the answers

    What is the annual repayment for a loan of £30,000 at an interest rate of 12% for 10 years?

    <p>£5,309.5</p> Signup and view all the answers

    What is the effective annual rate for a flat rate of 10% with monthly compounding?

    <p>10.47%</p> Signup and view all the answers

    What is the formula for the present value of a perpetuity?

    <p>PV = C / r</p> Signup and view all the answers

    What happens to the effective interest rate when the compounding frequency increases?

    <p>It increases</p> Signup and view all the answers

    What is the formula for the future value of an investment with compounding?

    <p>FV = PV x (1 + r)^t</p> Signup and view all the answers

    What is the advantage of using effective annual rates?

    <p>It makes calculations simpler</p> Signup and view all the answers

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

    <p>PV = C x ((1 - 1/(1 + r)^t) / r)</p> Signup and view all the answers

    What is the difference between the nominal interest rate and the real interest rate?

    <p>The nominal rate is higher</p> Signup and view all the answers

    What is the concept when £100 now is worth more than £100 in one year's time?

    <p>Time value of money</p> Signup and view all the answers

    What is the formula to calculate the future value of an investment?

    <p>FV = PV x (1 + r)^t</p> Signup and view all the answers

    What happens to the investment when it earns interest over a period?

    <p>Its value grows</p> Signup and view all the answers

    What is the interest rate used in the calculation of the future value?

    <p>Decimal form of the percentage</p> Signup and view all the answers

    What is the result of investing £1000 at 12% per year for 2 years?

    <p>£1304.80</p> Signup and view all the answers

    Why do we use 0.12 instead of 12% in calculations?

    <p>To convert the percentage to a decimal</p> Signup and view all the answers

    What is the concept underlying the time value of money?

    <p>A pound today is worth more than a pound in the future</p> Signup and view all the answers

    What is the difference between the principal and the future value?

    <p>The principal is the amount invested, and the future value is the principal plus interest</p> Signup and view all the answers

    What is the purpose of the formula FV = PV (1 + r)t?

    <p>To calculate the future value</p> Signup and view all the answers

    If an investment doubles in 5 years, what is the interest rate?

    <p>14.87%</p> Signup and view all the answers

    What is the present value of a series of cash flows of £2500, £900, and £3600 at the end of year 1, 4, and 6, respectively, at a rate of 9%?

    <p>£5077.7</p> Signup and view all the answers

    What is the formula for the present value of an annuity of C at the end of each of the next t years at r per year?

    <p>PV = C x (1 - (1+r)^(-t)) / r</p> Signup and view all the answers

    What is the future value of a series of cash flows of £2500, £900, and £3600 at the end of year 1, 4, and 6, respectively, at a rate of 9% after 7 years?

    <p>£9282.3</p> Signup and view all the answers

    What is the purpose of the formula r = (FV/PV)^(1/t) - 1?

    <p>To calculate the interest rate</p> Signup and view all the answers

    What is the relationship between the interest rate and the number of years?

    <p>The interest rate increases as the number of years increases</p> Signup and view all the answers

    What is the purpose of the formula PV = C x (1 - (1+r)^(-t)) / r?

    <p>To calculate the present value of an annuity</p> Signup and view all the answers

    What is the difference between compound interest and simple interest?

    <p>Compound interest is applied to both principal and interest, while simple interest is only applied to the principal.</p> Signup and view all the answers

    What is the formula for the future value of an investment?

    <p>FV = PV x (1 + r)^t</p> Signup and view all the answers

    How does the interest rate affect the future value of an investment?

    <p>A higher interest rate increases the future value.</p> Signup and view all the answers

    What is the purpose of discounting?

    <p>To determine the present value of a future cash flow.</p> Signup and view all the answers

    What is the effect of compounding frequency on the future value of an investment?

    <p>More frequent compounding increases the future value.</p> Signup and view all the answers

    What is the relationship between the nominal interest rate and the effective interest rate?

    <p>The nominal interest rate is always higher than the effective interest rate.</p> Signup and view all the answers

    How does the time period of an investment affect the future value?

    <p>A longer time period increases the future value.</p> Signup and view all the answers

    What is the present value of a cash flow?

    <p>The value today of a future cash flow, discounted by the interest rate.</p> Signup and view all the answers

    What is the relationship between the real rate and the nominal rate?

    <p>Real rate = Nominal rate - Inflation rate</p> Signup and view all the answers

    What is the process of calculating the present value?

    <p>Discounting</p> Signup and view all the answers

    What happens to the effective interest rate when the compounding frequency increases?

    <p>It increases</p> Signup and view all the answers

    What is the formula for calculating the future value?

    <p>FV = PV (1 + r)t</p> Signup and view all the answers

    What is an annuity?

    <p>A series of cash flows at regular intervals</p> Signup and view all the answers

    What is the real cash payoff if the nominal cash payoff is £110 and the inflation rate is 7%?

    <p>£102.8</p> Signup and view all the answers

    What is the difference between the nominal interest rate and the real interest rate?

    <p>The nominal rate includes inflation, while the real rate excludes it</p> Signup and view all the answers

    What is the process of calculating the future value?

    <p>Compounding</p> Signup and view all the answers

    What is the present value of £25,000 in 3 months' time if the interest rate is 1.125%?

    <p>£24,274.6</p> Signup and view all the answers

    If you borrow £100 at an APR of 4200% and make no repayments, how much would you owe after 2 years?

    <p>£180,000</p> Signup and view all the answers

    What is the future value of £100 invested at 11% for 1 year, 9% for 2 years, and 13% for 3 years?

    <p>£136.72</p> Signup and view all the answers

    What is the present value of £100 in 4 years' time if the interest rates are 8% for year 1, 12% for year 2, 6% for year 3, and 13% for year 4?

    <p>£69.01</p> Signup and view all the answers

    What is the real return on an investment if you invest £100 for a year at 10% interest, and inflation is 7%?

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

    If you invest £100 for a year at 10% interest, and inflation is 7%, how much can you buy at the end of the year?

    <p>107 copies</p> Signup and view all the answers

    What is the nominal interest rate that is equivalent to a real interest rate of 3% and an inflation rate of 7%?

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

    What is the relationship between the nominal interest rate and the real interest rate?

    <p>The nominal interest rate is greater than the real interest rate</p> Signup and view all the answers

    What is the effect of compounding on the effective interest rate?

    <p>The effective interest rate increases</p> Signup and view all the answers

    What is the annual percentage rate (APR) that is equivalent to an effective annual rate (EAR) of 16%?

    <p>16%</p> Signup and view all the answers

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