Question

1. What is the biannual effective discount rate corresponding to a nominal interest rate of 11% convertible every two years?

2. What is the accumulated value at 10 years of 10 payments increasing arithmetically from $11 at the end of year 1 to $20 at the end of year 10 given an annual interest rate of 4%.

3. Elizabeth agrees to sell her matchbook collection for its fair market value and receives a down payment of $100 today plus a promise of $200 to be paid at the end of year 1, $400 to be paid at the end of year 2, $600 to be paid at the end of year 3, $800 at the end of year 4, and her final payment of $1,000 at the end of year 5. What is the fair market value of Elizabeth’s matchbook collection on the day she sells it assuming an annual effective interest rate of 10%.

Answer 1

What is the biannual effective discount rate corresponding to a nominal interest rate of 11% convertible every two year
Discount Rate = 1-(1-22%/4)^4	20.25%

What is the accumulated value at 10 years of 10 payments increasing arithmetically from $11 at the end of year 1 to $20 at the end of year 10 given an annual interest rate of 4%.
F = 1(A/G,4%,10)
F = 1 x 4.177	4.177
F = 10 + 4.177	14.177
Elizabeth agrees to sell her matchbook collection for its fair market value and receives a down payment of $100 today plus a promise of $200 to be paid at the end of year 1, $400 to be paid at the end of year 2, $600 to be paid at the end of year 3, $800 at the end of year 4, and her final payment of $1,000 at the end of year 5. What is the fair market value of Elizabeth’s matchbook collection on the day she sells it assuming an annual effective interest rate of 10%.
Year	Payment	PV @ 10%	Present Value
0	100	1.000	$     100.00
1	200	0.909	$     181.82
2	400	0.826	$     330.58
3	600	0.751	$     450.79
4	800	0.683	$     546.41
5	1000	0.621	$     620.92
		Fair Value	$  2,230.52