Question

(a) Starting from today, every month you save $200 into a bank account which earns interest at annual rate of 3.8%.

How much money do you have in the account at the end of 8 years?

(b) What is the modified duration of an 6% bond with 11 years to maturity that is trading at a yield of 6%?

Assume that coupon is paid semi-annually.

(c) Suppose that the 6-month US Treasury bill rate is equal to 5.98%, and the forward rate on a 6-month Treasury bill 6 months from now is 7.88%. (Both are in yearly terms).

What is the 1-year bill rate?

Answer 1

(a) Interest will be calculated using below formula

I = P * r * t

where p= principle amount $ 200 *12 = 2400

r= 3.8% ( given that bank will pay interest annually)

t = time period 1 year

year 1 interest will be received for 8 years

(200*12) * 3.8/100 * 1 = 91.2 * 8 years = 729 ( for all 8 years )

for year 2's saving interest will be received for remaining 7 years i.e 91.2*7 = 638.4 ( for year 2,3,4,5,6,7,8)

for year 3's saving interest will be received for remaining 6 years i.e 91.2*6 = 547.2 ( for year ,3,4,5,6,7,8)

for year 4's saving interest will be received for remaining 5 years i.e 91.2*5 = 456 ( for year ,4,5,6,7,8)

for year 5's saving interest will be received for remaining 4 years i.e 91.2*4 = 364.8    ( for year ,5,6,7,8)

for year 6's saving interest will be received for remaining 3 years i.e 91.2*3 = 273.6    ( for year ,6,7,8)

for year 7's saving interest will be received for remaining 7 years i.e 91.2*2 = 182.4 ( for year ,7,8)

for year 8's saving interest will be received for remaining 7 years i.e 91.2*1= 91.2    ( for year ,8)

total interest after 8 years will be 729 + 638.4+ 547.2 +456 + 364.8 + 273.6 + 182.4+ 91.2 = 3282.6

and principal amount which is your saving will be 200*12*8 = 19200

total amount you will have after 8 years will be 19200+3282.6 = 22482.6

(b) modified duration of the bond will be calculated by formula

where y is yield to maturity 6%

and m is number of payment it is semi annually hence it will be 2 ( 6 months and 6 months )

= 10.67 will be modified duration

(c) please raise this as separate question