Time Value of Money Lectures 3 & 4

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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?

£131.69 Signup and view all the answers

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

EAR is always greater than the flat rate Signup and view all the answers

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

To simplify discounting and compounding for periods other than multiples of a year Signup and view all the answers

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

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

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

The EAR increases Signup and view all the answers

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

Because of the opportunity to invest it at a positive interest rate Signup and view all the answers

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

£540 Signup and view all the answers

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

It increases the future value Signup and view all the answers

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

The effective annual rate is always higher than the nominal interest rate 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?

£1,091.01 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?

£2,498.40 Signup and view all the answers

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

It depends on the investment period Signup and view all the answers

What is the difference between real and nominal interest rates?

The real interest rate is adjusted for inflation, while the nominal interest rate is not Signup and view all the answers

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

16554.1 Signup and view all the answers

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

16 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?

£13,000,000,000 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?

136.72 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%?

69.02 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%?

3% 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%?

17% 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?

24274.6 Signup and view all the answers

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

r = [FV/PV]1/t - 1 Signup and view all the answers

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

10.48% Signup and view all the answers

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

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

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

10.29 years Signup and view all the answers

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

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

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

£12,456.1 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?

£3,841.9 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?

£7,531.2 Signup and view all the answers

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

FV = PV × (1 + r)^t Signup and view all the answers

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

Real rate = Nominal rate - Inflation rate Signup and view all the answers

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

It increases the effective interest rate Signup and view all the answers

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

Discounting 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%?

£110 Signup and view all the answers

What is the difference between an annuity and a perpetuity?

An annuity has a fixed time period, while a perpetuity has an infinite time period 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%?

Real cash payoff = Nominal cash payoff ÷ (1 + Inflation rate) Signup and view all the answers

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

The interest rate is exponentially related to the time period Signup and view all the answers