Continuous compounding is an important theoretical concept in Finance. Let i be the annual nominal interest...

 

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Continuous compounding is an important theoretical concept in Finance. Let i be the annual nominal interest rate. (a) State a formula for the future value FV of an investment with present value PV which is compounded with compounding frequency m for n years. (1 mark) (b) State a formula for the future value FV of an investment with present value PV which is compounded with continuous compounding for n years. (1 mark) (c) Show that the formula in (a) approaches the formula in (b) as the compounding frequency m approaches infinity. (3 marks) (d) State a formula for the effective annual interest rate of an investment which is compounded with compounding frequency m. (1 mark) (e) State a formula for the effective annual interest rate of an investment which is compounded with continuous compounding. (1 mark) (f) Show that the formula in (d) approaches the formula in (e) as the compounding frequency m approaches infinity. (3 marks) (g) For an investment of $1,000 with interest rate 10% per annum, calculate the future value FV after one year with continuous compounding. (2 marks) (h) Explain why the All Ordinaries Index is the broadest index on the Australian Securities Exchange. (3 marks) (3 marks) (i) Does the All Ordinaries Index compound continuously? Explain your answer. Continuous compounding is an important theoretical concept in Finance. Let i be the annual nominal interest rate. (a) State a formula for the future value FV of an investment with present value PV which is compounded with compounding frequency m for n years. (1 mark) (b) State a formula for the future value FV of an investment with present value PV which is compounded with continuous compounding for n years. (1 mark) (c) Show that the formula in (a) approaches the formula in (b) as the compounding frequency m approaches infinity. (3 marks) (d) State a formula for the effective annual interest rate of an investment which is compounded with compounding frequency m. (1 mark) (e) State a formula for the effective annual interest rate of an investment which is compounded with continuous compounding. (1 mark) (f) Show that the formula in (d) approaches the formula in (e) as the compounding frequency m approaches infinity. (3 marks) (g) For an investment of $1,000 with interest rate 10% per annum, calculate the future value FV after one year with continuous compounding. (2 marks) (h) Explain why the All Ordinaries Index is the broadest index on the Australian Securities Exchange. (3 marks) (3 marks) (i) Does the All Ordinaries Index compound continuously? Explain your answer.

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