Question

1. Find the present value of a ten-year annuity which pays $600 at the beginning of each quarter for the first 5 years, and then $500 at the beginning of each quarter for the remaining years. The annual effective interest rate is 5%. Round your answer to two decimal places.

2. A bank makes payments continuously at a rate of $260 per year. The payments are made between times 6 and 9 (measured in years). Find the present value of these payments at time 2 using an annual effective rate of discount of 6%. Round your answer to two decimal places.

pls show all steps and work

Answer 1

1. Calculate the Present value. Quarterly payments = 600 for 1 to 5 years and 500 for 6 to 10 years rate 5%. Payments are at beginning of Quarter.

You need Quarterly rate Given EAR = 5%

=

= 1.227223% Quartely

Present Value is 17708.72. Calculation as below

Year End	Payments	PV Factor @ 1.227223%	Present Value
0.00	600.00	1.00000	600.00
1.00	600.00	0.98788	592.73
2.00	600.00	0.97590	585.54
3.00	600.00	0.96407	578.44
4.00	600.00	0.95238	571.43
5.00	600.00	0.94083	564.50
6.00	600.00	0.92943	557.66
7.00	600.00	0.91816	550.90
8.00	600.00	0.90703	544.22
9.00	600.00	0.89603	537.62
10.00	600.00	0.88517	531.10
11.00	600.00	0.87444	524.66
12.00	600.00	0.86384	518.30
13.00	600.00	0.85336	512.02
14.00	600.00	0.84302	505.81
15.00	600.00	0.83280	499.68
16.00	600.00	0.82270	493.62
17.00	600.00	0.81273	487.64
18.00	600.00	0.80288	481.73
19.00	600.00	0.79314	475.89
20.00	500.00	0.78353	391.76
21.00	500.00	0.77403	387.01
22.00	500.00	0.76464	382.32
23.00	500.00	0.75537	377.69
24.00	500.00	0.74622	373.11
25.00	500.00	0.73717	368.58
26.00	500.00	0.72823	364.12
27.00	500.00	0.71940	359.70
28.00	500.00	0.71068	355.34
29.00	500.00	0.70207	351.03
30.00	500.00	0.69355	346.78
31.00	500.00	0.68515	342.57
32.00	500.00	0.67684	338.42
33.00	500.00	0.66863	334.32
34.00	500.00	0.66053	330.26
35.00	500.00	0.65252	326.26
36.00	500.00	0.64461	322.30
37.00	500.00	0.63679	318.40
38.00	500.00	0.62907	314.54
39.00	500.00	0.62145	310.72
			17708.72

2. Calculate the pv at Time 2. Payments $260 at 6th 7th 8th and 9th years rate 6%

= 205.94 + 194.29 + 183.29+172.91

= 756.44