Question

1.Deposits of $1000 are made at the beginning of each year for three years. The balance at the end of each year (before the deposit for the next year) was $1100, $2000, and $3400, respectively. Find the time-weighted yield rate.

2. A 10,000 par value 10-year bond with 8% annual coupons is bought at a premium to yield an annual effective rate of 6%. Calculate the interest portion of the 7th coupon.

Answer 1

Answer 1. Formula to calculate time weighted yield rate is

Time-weighted yield = [(1+i₁) * (1+i₂) * (1+i₃) * ……. (1+i_N)] – 1

Where i_n is rate of return on time period n,

i_n = (End Balance of time period n – (Starting Balance of time period n + Cash Flow during the period)) /( Starting Balance of time period n + Cash Flow during the period)

Hence, i₁ = (1100 – (0 + 1000))/(1000 + 0) = 100/1000 = 0.1

i₂ = (2000 – (1100 + 1000)) / (1100 + 1000) = -100/2100 = -.04762

i₃ = (3400 – (2000 + 1000)) / (2000 + 1000) = 400/3000 = .13333

Hence

Time-weighted yield = [(1+0.1) * (1-.04762) * (1+.1333)] – 1

= 1.1 * 0.95832 * 1.13333 – 1 = 1.1873 – 1 = .1873 = 18.73%

Time-weighted yield rate = 18.73%

Answer 2.

Price of Bond = 800 * PVIFA (6%, 10) + 10000/(1+6%)^10 = 800 * 7.360087 + 5583.95 = 11472.01

Year	Starting Bal	Interest	Principal	Closing Bal
1	11472.01	688.32	111.68	11360.33
2	11360.33	681.62	118.38	11241.95
3	11241.95	674.52	125.48	11116.47
4	11116.47	666.99	133.01	10983.46
5	10983.46	659.01	140.99	10842.47
6	10842.47	650.55	149.45	10693.02
7	10693.02	641.58	158.42	10534.6
8	10534.6	632.08	167.92	10366.68
9	10366.68	622	178	10188.68
10	10188.68	611.32	188.68	10000

Hence, interest portion on 7^th coupon is $641.58