Compound Interest Calculation

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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?

£2593.7 (C) Signup and view all the answers

What is the difference between compound interest and simple interest?

Compound interest applies to both principal and interest, while simple interest applies to the original principal. (A) Signup and view all the answers

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

£1488.0 (A) Signup and view all the answers

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

£1801.8 (A) Signup and view all the answers

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

£1801.8 (B) Signup and view all the answers

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

r = (FV/PV)^(1/t) - 1 (B) 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%?

5 years (B) 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%?

5077.7 (B) 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?

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

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

£18,491.5 (A) 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?

9282.3 (B) Signup and view all the answers

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

14.87% (B) Signup and view all the answers

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

To find the interest rate of an investment (D) Signup and view all the answers

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

16554.1 (A) Signup and view all the answers

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

16% (C) 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%?

7,500,000 (D) 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?

136.72 (A) 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?

69.02 (C) 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%?

3% (A) 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%?

10% (A) 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?

107 copies of a newspaper (B) Signup and view all the answers

What is the process of calculating the present value?

Discounting (C) Signup and view all the answers

What is the relationship between real rate and nominal rate?

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

What is the formula for calculating the future value?

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

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

It increases (C) Signup and view all the answers

What is an annuity?

A series of payments (C) 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%?

£102.8 (B) Signup and view all the answers

What is the process of calculating the future value?

Compounding (A) Signup and view all the answers

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

The inflation rate (D) Signup and view all the answers

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

PV = C / r (B) Signup and view all the answers

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

10.25% (C) 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?

£10.47 (A) Signup and view all the answers

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

FV = C * (1 + r/m)^(m*t) (D) 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?

£5,309.5 (C) Signup and view all the answers

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

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

What is the advantage of using effective annual rates?

They are used for discounting and compounding for periods other than multiples of a year. (D) Signup and view all the answers

What is the annuity where the cash flows continue forever?

Perpetuity (A) 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?

£5,309.5 (A) Signup and view all the answers

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

10.47% (B) Signup and view all the answers

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

PV = C / r (A) Signup and view all the answers

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

It increases (A) Signup and view all the answers

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

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

What is the advantage of using effective annual rates?

It makes calculations simpler (A) Signup and view all the answers

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

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

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

The nominal rate is higher (B) Signup and view all the answers

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

Time value of money (A) Signup and view all the answers

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

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

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

Its value grows (B) Signup and view all the answers

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

Decimal form of the percentage (A) Signup and view all the answers

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

£1304.80 (A) Signup and view all the answers

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

To convert the percentage to a decimal (A) Signup and view all the answers

What is the concept underlying the time value of money?

A pound today is worth more than a pound in the future (B) Signup and view all the answers

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

The principal is the amount invested, and the future value is the principal plus interest (C) Signup and view all the answers

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

To calculate the future value (B) Signup and view all the answers

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

14.87% (B) 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%?

£5077.7 (D) 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?

PV = C x (1 - (1+r)^(-t)) / r (A) 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?

£9282.3 (B) Signup and view all the answers

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

To calculate the interest rate (A) Signup and view all the answers

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

The interest rate increases as the number of years increases (D) Signup and view all the answers

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

To calculate the present value of an annuity (B) Signup and view all the answers

What is the difference between compound interest and simple interest?

Compound interest is applied to both principal and interest, while simple interest is only applied to the principal. (A) Signup and view all the answers

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

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

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

A higher interest rate increases the future value. (A) Signup and view all the answers

What is the purpose of discounting?

To determine the present value of a future cash flow. (A) Signup and view all the answers

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

More frequent compounding increases the future value. (B) Signup and view all the answers

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

The nominal interest rate is always higher than the effective interest rate. (A) Signup and view all the answers

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

A longer time period increases the future value. (A) Signup and view all the answers

What is the present value of a cash flow?

The value today of a future cash flow, discounted by the interest rate. (B) Signup and view all the answers

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

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

What is the process of calculating the present value?

Discounting (A) Signup and view all the answers

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

It increases (B) Signup and view all the answers

What is the formula for calculating the future value?

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

What is an annuity?

A series of cash flows at regular intervals (B) 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%?

£102.8 (B) Signup and view all the answers

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

The nominal rate includes inflation, while the real rate excludes it (A) Signup and view all the answers

What is the process of calculating the future value?

Compounding (B) 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%?

£24,274.6 (A) 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?

£180,000 (C) 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?

£136.72 (D) 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?

£69.01 (C) 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%?

3% (D) 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?

107 copies (C) 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%?

10% (A) Signup and view all the answers

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

The nominal interest rate is greater than the real interest rate (D) Signup and view all the answers

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

The effective interest rate increases (D) Signup and view all the answers

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

16% (C) Signup and view all the answers

Compound Interest Calculation

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Questions and Answers

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

What is the total interest earned in the second period?

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

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

What is the difference between compound interest and simple interest?

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

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

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

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

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

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%?

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?

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

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?

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

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

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

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

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

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?

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?

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

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

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?

What is the process of calculating the present value?

What is the relationship between real rate and nominal rate?

What is the formula for calculating the future value?

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

What is an annuity?

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

What is the process of calculating the future value?

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

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

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

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

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

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

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

What is the advantage of using effective annual rates?

What is the annuity where the cash flows continue forever?

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

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

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

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

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

What is the advantage of using effective annual rates?

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

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

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

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

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

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

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

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

What is the concept underlying the time value of money?

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

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

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

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%?

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?

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?

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

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

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

What is the difference between compound interest and simple interest?

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

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

What is the purpose of discounting?

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

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

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

What is the present value of a cash flow?

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

What is the process of calculating the present value?

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

What is the formula for calculating the future value?