7. Assume Emily invested $60,000 in the short-term fund, $40,000 in the intermediate-term fund, and $100,000 in the total bond fund. What would be the duration of her overall bond portfolio? Explain your answer.

Vanguard mutual funds (ticker is in parentheses)
	Short-term (VBIRX)	Intermediate-term (VBILX)	Long-term (VBLAX)	Total Bond Market (VBTLX)	High-yield Corporate (VWEAX)
Distribution by credit quality (% of fund)	--------	--------	--------	--------	--------
U.S. Govt.	64.0	49.3	39.4	59.5	5.8
Aaa	5.0	2.1	1.7	3.8	0
Aa	3.7	3.5	6.2	3.6	0
A	12.9	18.2	21.4	12.7	0
Baa	14.4	26.9	31.4	20.4	0
< Baa	0	0	0	0	90.9
Other	0	0	0	0	3.3
Expense Ratio	0.07%	0.07%	0.07%	0.05%	0.13%
Yield to maturity	0.40%	1.10%	3.00%	1.10%	3.9%
30 day SEC yield	0.29%	1.08%	2.87%	1.08%	3.10%
Average duration (Years)	2.7	6.5	15.6	6.7	3.7
Number of bonds	2,660	2,129	2,707	9,995	599