40 Questions
What is the annual repayment if you borrow £30,000 at a 12% interest rate for 10 years?
£5,309.5
What is the present value of a perpetuity with a cash flow of £1,000 per year, given an interest rate of 12%?
£83.33
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?
10.25%
What is the future value of £100 invested for 3 years at a flat rate of 10% per year with semiannual compounding?
£131.69
What is the relationship between the flat rate and the effective annual rate (EAR)?
EAR is always greater than the flat rate
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
What is the formula to calculate the future value of an investment with compounding?
FV = C (1 + r/m)^(mt)
What is the effect of increasing the compounding frequency on the effective annual rate (EAR)?
The EAR increases
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
What is the future value of a single investment of £500 at 8% per year for 1 year?
£540
What is the effect of compounding periods on the future value of an investment?
It increases the future value
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
What is the present value of £1,200 to be received in 1 year's time, discounted at 10% per year?
£1,091.01
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
What is the effect of non-constant interest rates on the future value of an investment?
It depends on the investment period
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
What is the present value of £25,000 in 3½ years at an interest rate of 1.125?
16554.1
What is the annual percentage rate equivalent to an effective annual rate of 16?
16
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
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
What is the present value of £100 in 4 years' time with interest rates of 8%, 12%, 6%, and 13%?
69.02
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%
What is the nominal interest rate equivalent to an effective annual rate of 10% with an inflation rate of 7%?
17%
What is the present value of £25000 at the end of 3 months at an interest rate of 1.125?
24274.6
What is the formula to solve for r when FV, PV, and t are given?
r = [FV/PV]1/t - 1
If an investment triples in 10 years, what is the approximate rate of return?
10.48%
What is the formula to find the present value of a series of cash flows?
PV = Σ[C / (1 + r)t]
If r = 0.05, how long does it take for an investment to double?
10.29 years
What is the formula to find the present value of an annuity?
PV = C × [1 - {1/(1+r)t}] / r
What is the present value of a 5-year annuity of £3000 at r = 10%?
£12,456.1
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
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
What is the formula to calculate the future value of a sum of money?
FV = PV × (1 + r)^t
What is the relationship between the real rate and the nominal rate?
Real rate = Nominal rate - Inflation rate
What is the effect of increasing the compounding frequency on the effective interest rate?
It increases the effective interest rate
What is the process of calculating the present value of a sum of money?
Discounting
What is the nominal cash payoff if the real cash payoff is £102.8 and the inflation rate is 7%?
£110
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
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)
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
Test your understanding of the time value of money concepts, including compound interest, future values, discounting, and present values. Learn about valuing multi-period cash flows, annuities, and perpetuities. Explore the effects of compounding periods, effective annual rates, and non-constant interest rates.
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