Time Value of Money Lectures 3 & 4
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Questions and Answers

What is the annual repayment if you borrow £30,000 at a 12% interest rate for 10 years?

  • £6,000
  • £5,309.5 (correct)
  • £4,500
  • £7,200

What is the present value of a perpetuity with a cash flow of £1,000 per year, given an interest rate of 12%?

  • £100
  • £91.67
  • £120
  • £83.33 (correct)

What is the effective annual rate (EAR) if you invest £100 for a year at a flat rate of 10% per year with semiannual compounding?

  • 10.47%
  • 10.25% (correct)
  • 11.00%
  • 10.00%

What is the future value of £100 invested for 3 years at a flat rate of 10% per year with semiannual compounding?

<p>£131.69 (D)</p> Signup and view all the answers

What is the relationship between the flat rate and the effective annual rate (EAR)?

<p>EAR is always greater than the flat rate (D)</p> Signup and view all the answers

What is the purpose of using effective annual rates (EAR) in finance?

<p>To simplify discounting and compounding for periods other than multiples of a year (A)</p> Signup and view all the answers

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

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

What is the effect of increasing the compounding frequency on the effective annual rate (EAR)?

<p>The EAR increases (D)</p> Signup and view all the answers

Why is £100 now worth more than £100 in one year's time?

<p>Because of the opportunity to invest it at a positive interest rate (D)</p> Signup and view all the answers

What is the future value of a single investment of £500 at 8% per year for 1 year?

<p>£540 (D)</p> Signup and view all the answers

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

<p>It increases the future value (B)</p> Signup and view all the answers

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

<p>The effective annual rate is always higher than the nominal interest rate (B)</p> Signup and view all the answers

What is the present value of £1,200 to be received in 1 year's time, discounted at 10% per year?

<p>£1,091.01 (B)</p> Signup and view all the answers

What is the future value of a series of annual investments of £1,000, made for 2 years, at 12% per year?

<p>£2,498.40 (A)</p> Signup and view all the answers

What is the effect of non-constant interest rates on the future value of an investment?

<p>It depends on the investment period (D)</p> Signup and view all the answers

What is the difference between real and nominal interest rates?

<p>The real interest rate is adjusted for inflation, while the nominal interest rate is not (C)</p> Signup and view all the answers

What is the present value of £25,000 in 3½ years at an interest rate of 1.125?

<p>16554.1 (D)</p> Signup and view all the answers

What is the annual percentage rate equivalent to an effective annual rate of 16?

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

If you borrow £100 at an APR of 4200%, how much will you owe after 5 years if you make no repayments?

<p>£13,000,000,000 (B)</p> Signup and view all the answers

What is the future value of an investment of £100 with interest rates of 11%, 9%, and 13% for the next three years?

<p>136.72 (A)</p> Signup and view all the answers

What is the present value of £100 in 4 years' time with interest rates of 8%, 12%, 6%, and 13%?

<p>69.02 (A)</p> Signup and view all the answers

If you invest £100 for a year at a nominal interest rate of 10%, what is your real return if the inflation rate is 7%?

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

What is the nominal interest rate equivalent to an effective annual rate of 10% with an inflation rate of 7%?

<p>17% (B)</p> Signup and view all the answers

What is the present value of £25000 at the end of 3 months at an interest rate of 1.125?

<p>24274.6 (A)</p> Signup and view all the answers

What is the formula to solve for r when FV, PV, and t are given?

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

If an investment triples in 10 years, what is the approximate rate of return?

<p>10.48% (A)</p> Signup and view all the answers

What is the formula to find the present value of a series of cash flows?

<p>PV = Σ[C / (1 + r)t] (C)</p> Signup and view all the answers

If r = 0.05, how long does it take for an investment to double?

<p>10.29 years (D)</p> Signup and view all the answers

What is the formula to find the present value of an annuity?

<p>PV = C × [1 - {1/(1+r)t}] / r (A)</p> Signup and view all the answers

What is the present value of a 5-year annuity of £3000 at r = 10%?

<p>£12,456.1 (B)</p> Signup and view all the answers

If you borrow £25,000 at an interest rate of 10% and plan to repay the loan using a 7-year annuity, what is the approximate annual payment?

<p>£3,841.9 (A)</p> Signup and view all the answers

What is the future value of a series of cash flows of £2000, £3000, and £4000 at the end of year 1, 2, and 3, respectively, at r = 0.08?

<p>£7,531.2 (A)</p> Signup and view all the answers

What is the formula to calculate the future value of a sum of money?

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

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

<p>It increases the effective interest rate (C)</p> Signup and view all the answers

What is the process of calculating the present value of a sum of money?

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

What is the nominal cash payoff if the real cash payoff is £102.8 and the inflation rate is 7%?

<p>£110 (D)</p> Signup and view all the answers

What is the difference between an annuity and a perpetuity?

<p>An annuity has a fixed time period, while a perpetuity has an infinite time period (A)</p> Signup and view all the answers

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

<p>Real cash payoff = Nominal cash payoff ÷ (1 + Inflation rate) (C)</p> Signup and view all the answers

What is the relationship between the interest rate and the time period in calculating the future value?

<p>The interest rate is exponentially related to the time period (A)</p> Signup and view all the answers

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