Question

1. An investment will pay $100 at the end of each of the next 3 years, $250 at the end of Year 4, $400 at the end of Year 5, and $550 at the end of Year 6. If other investments of equal risk earn 12% annually, what is its present value? Its future value? Do not round intermediate calculations. Round your answers to the nearest cent.

2.You want to buy a car, and a local bank will lend you $30,000. The loan will be fully amortized over 5 years (60 months), and the nominal interest rate will be 5% with interest paid monthly. What will be the monthly loan payment? What will be the loan's EAR? Do not round intermediate calculations. Round your answer for the monthly loan payment to the nearest cent and for EAR to two decimal places.

3.

Find the following values using the equations and then a financial calculator. Compounding/discounting occurs annually. Do not round intermediate calculations. Round your answers to the nearest cent.

An initial $300 compounded for 1 year at 5%.

$  

An initial $300 compounded for 2 years at 5%.

$  

The present value of $300 due in 1 year at a discount rate of 5%.

$  

The present value of $300 due in 2 years at a discount rate of 5%.

4.

Answer 1

1)
	a.	Present Value	$              904.68
	Working:
	Year	Cash flow	Present Value of 1	Present Value of cash flow
	a	b	c=1.12^-a	d=b*c
	1	$                  100	0.8929	$            89.29
	2	$                  100	0.7972	$            79.72
	3	$                  100	0.7118	$            71.18
	4	$                  250	0.6355	$          158.88
	5	$                  400	0.5674	$          226.97
	6	$                  550	0.5066	$          278.65
		Total		$          904.68
	b.	Future Value	$          1,785.68
	Working:
	Year	Cash flow	Future Value of 1	Future Value of cash flow
	a	b	c=1.12^(6-a)	d=b*c
	1	$                  100	1.7623	$          176.23
	2	$                  100	1.5735	$          157.35
	3	$                  100	1.4049	$          140.49
	4	$                  250	1.2544	$          313.60
	5	$                  400	1.1200	$          448.00
	6	$                  550	1.0000	$          550.00
		Total		$      1,785.68
2)
	a.	Monthly Payment		$          566.14
		Working:
		Present value of annuity of 1		=	(1-(1+i)^-n)/i			Where,
				=	(1-(1+0.004167)^-60)/0.004167			i	5%/12	=	0.004167
				=	52.99019			n	60
		Monthly Payment		=	Loan amount / Present value of annuity of 1
				=	$       30,000	/	52.99019
				=	$       566.14
	b.	EAR	5.12%
		Working:
		EAR		=	((1+(i/n))^n)-1		Where,
				=	((1+(0.05/12))^12)-1		i	5%	(Yearly return)
				=	5.12%		n	12	(Number of times compounding in a year)
3)
	a.	Future Value	$              315.00
	Working:
		Future Value		=	300*(1+0.05)^1
				=	$       315.00
	b.	Future Value	$              330.75
	Working:
		Future Value		=	300*(1+0.05)^2
				=	330.75
	c.	Present Value	$              285.71
	Working:
		Present Value		=	300*(1+0.05)^-1
				=	$       285.71
	d.	Present Value	$              272.11
	Working:
		Present Value		=	300*(1+0.05)^-2
				=	$       272.11