Question

Exercise 5-9 (Algo) Present value; annuities [LO5-8) Using the appropriate present value table and assuming a 12% annual Interest rate, determine the present value on December 31, 2021, of a five-period annual annuty of $2900 under each of the following situations: (Ev.of $1, PV of $1. FVA of $1. PVA of $1. FVAD of $1 and PVAD of $1) (Use appropriete fector(s) from the tables provided.) ed 1. The first payment is received on December 31, 2022 and interest is compounded annually. 2. The first payment is received on December 31, 2021, and interest is compounded annually. 3. The first payment is received on December 31, 2022 and interest is compounded quarterly. Complete this question by entering your answers in the tabs below. Required 3 Required 1 Required 2 The first payment is received on December, 31, 2022, and interest is compounded annually. (Round your final answers to nearest whole dollar amount.) nces Table or caloulator function Payment PV-12/31/20213 Required 2

Answer 1

Solution 1:

PV Factor based on
Table or Calculator function	PVA of $1
Payment	$2,900
n=	5
i=	12.00%
PV factor	3.60578
PV -12/31/2021	$10,457

Solution 2:

PV Factor based on
Table or Calculator function	PVAD of $1
Payment	$2,900
n=	5
i=	12.00%
PV factor	4.03735
PV -12/31/2021	$11,708

Solution 3:

Quarterly interest rate = 12%/4 = 3%

Effective annual interest rate = 1 *(1+0.03)^4 - 1= 12.55%

Deposit Date	i=	n=	Deposit	PV Factor	Present Value
31-Dec-22	12.55%	1	$2,900.00	0.88849	$2,577
31-Dec-23	12.55%	2	$2,900.00	0.78942	$2,289
31-Dec-24	12.55%	3	$2,900.00	0.70140	$2,034
31-Dec-25	12.55%	4	$2,900.00	0.62319	$1,807
31-Dec-26	12.55%	5	$2,900.00	0.55370	$1,606
Total					$10,313