What is the relationship between the value of an annuity and discount rates? suppose you bought...

What is the relationship between the value of an annuity and discount rates? suppose you bought a 20 year annuity of 4700 per year at the current discount rate of 10 percent per year. what happens to the value of your investment if the discount rate suddenly drops to 5 percent? what if the discount rate suddenly rises to 15 percent?

Expert Solution

	Value of investment at 10%	P×[1-(1÷(1+r)^n)]÷r

	Here,

A	Interest rate per annum	10.00%
B	Number of years	20
C	Number of compoundings per per annum	1
A÷C	Interest rate per period ( r)	10.00%
B×C	Number of periods (n)	20
	Payment per period (P)	$ 4,700

	Value of investment at 10%	$ 40,013.75
		4700×(1-(1÷(1+10%)^20))÷10%

	Value of investment at 5%	P×[1-(1÷(1+r)^n)]÷r

	Here,

A	Interest rate per annum	5.00%
B	Number of years	20
C	Number of compoundings per per annum	1
A÷C	Interest rate per period ( r)	5.00%
B×C	Number of periods (n)	20
	Payment per period (P)	$ 4,700

	Value of investment at 5%	$ 58,572.39
		4700×(1-(1÷(1+5%)^20))÷5%

	Value of investment at 15%	P×[1-(1÷(1+r)^n)]÷r

	Here,

A	Interest rate per annum	15.00%
B	Number of years	20
C	Number of compoundings per per annum	1
A÷C	Interest rate per period ( r)	15.00%
B×C	Number of periods (n)	20
	Payment per period (P)	$ 4,700

	Value of investment at 15%	$ 29,418.86
		4700×(1-(1÷(1+15%)^20))÷15%

jeff jeffy answered 1 year ago

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