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zhiyan.zheng · 2021年08月24日

bond的计算是否有误?

NO.PZ2018091705000033

问题如下:

Tom has $100,000 stocks and $100,000 bonds. The $100,000 stocks are in the tax-deferred account and the $100,000 bonds are in the taxable account. We assume that:

1. The stock will provide 6% annually return.

2. The bond will provide 3% annually return.

3. Stock returns in taxable account will be taxed as whole deferred capital gains at a 15% percent rate. Interest income in taxable account is at 30 percent for each year.

4. Contributions in Tax-deferred account are not taxed, but withdrawals from this account will be taxed at 30 percent.

5. Cost basis is equal to 1

Calculate the post-tax value of Tom’s investment after 15 years.

选项:

A.

$304,339

B.

$369,076

C.

$209,876

解释:

A is correct.

考点Types of investment accounts

解析我们先算得放在交税账户中的债券投资在15年后的终值

FVtaxble=100,000[1+0.03(10.3)]15=136,580FV_{taxble}=100,000{\lbrack{1+0.03(1-0.3)}\rbrack}^{15}=136,580

接着我们继续算得放在递延账户中的股票投资在15年后的终值

FVTDA=100,000(1+0.06)15(10.3)=167,759FV_{TDA}=100,000{(1+0.06)}^{15}{(1-0.3)}=167,759

最后我们把两个资产账户的终值相加便得到Tom15年后投资的总市值

136580 + 167759 = 304,339

这里bond的就算用的15次方计算的复利,表示interest没有被拿出来而是变成了下一年的本金越滚越大,但正常的bond除非是PIK,不然interest是不会加到本金里继续滚的,是否应该将15次方改为乘以15?

1 个答案

王暄_品职助教 · 2021年08月24日

不用,因为文中给的是annual return,我们就默认复利即可。