Joe can purchase one of two annuities. Annuity 1: A 10 year decreasing annuity immediate with...

Joe can purchase one of two annuities.
Annuity 1: A 10 year decreasing annuity immediate with annual payments
of 10, 9, 8, ..., 2, 1.
Annuity 2: A perpetuity immediate with annual payments: the perpetuity
pays 1 in year 1, 2 in year 2, 3 in year 3, ...., 11 in year 11. After year 11, the
payments remain constant at 11.
At an annual e§ective interest rate of i, the present value of Annuity 2 is
twice the present value of Annuity 1. Calculate the present value of Annuity 1
at this annual e§ective interest rate of i.

Solutions

Expert Solution

We use excel solver to solve the problem

Initially, we assume any random effective interest rate of i ( 5% assumed)

Here, we find the terminal value using the formula = Annuity in year 11 + (Annuity in year 11 /Interest rate)

NPV is found using NPV function in excel => NPV = NPV (Interest rate, All cash-flows)

We input the following constraints in excel solver

Solving we get the Effective interest rate = 9.30% and PV of Annuity 1 = $39.42

Effective interest rate 'i' =	9.30%

	NPV	$39.42	$78.84
	Year
	1	10	1
	2	9	2
	3	8	3
	4	7	4
	5	6	5
	6	5	6
	7	4	7
	8	3	8
	9	2	9
	10	1	10
	Terminal value at year 11	0	129.2593

Hence, the Present Value of Annuity 1 at the required annual effective interest rate of 9.30% = $39.42

jeff jeffy answered 1 year ago

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