Question

Find the following present values on October 31, 2020.

a) Canadian T-bill maturing for $1.2 million in 273 days based on a yield rate of 1.25%

b) $10,000 due on March 31, 2025 at a force of interest of 5%

c) $3,600 due on April 30, 2022 at a nominal rare of discount of 6%, compounded 6 times a year.

d) Payments on $10,000 made every November 1 from 2020 to 2025 at 6.5% interest.

Answer 1

a)
Yield rate 1.25 for 365 days
Yield rate is 0.935% for 273 days
PVIF @ 0.935% is1/(1.00935)=0.99073
Present value of 1.2 Million note is 0.99073*1.2M=1.888Million
b)
PVIF @ 5% is 1/(1.05)^4.41666=0.806147
Present value of 10000 maturing at 31.03.2025 is 10000*0.806147=8061.47
PVIF=1/(1+r)^n
r=rate
n= number of periods
In this case no. of years is 4 years and 5 months which comes to 4.41666
c)
It is said in the question that the compounding period is 2 months( i.e, 6 times in a year)
Period between 31.10.2020 and 30.04.2022 is 18 months. That means, n=18/2=9
Rate is 6% for 12 months then 1% for 2 months
PVIF @ 1%, 9=1/(1.01)^9=0.91434
Present value of 3600 on 31.04.2022 is 3600*0.91434=3291.624
d)
Year	PVIF @ 6.5%	Installement	DCF
0	1.00	10,000.00	10,000.00
1	0.94	10,000.00	9,389.67
2	0.88	10,000.00	8,816.59
3	0.83	10,000.00	8,278.49
4	0.78	10,000.00	7,773.23
			44,257.99
Present value of installement is 44258