Answer:
the question is missing the information about potential investments, so I looked for a similar one:
5 Years 18 Years
Corporate bonds 5.75% 4.75%
(ordinary interest taxed annually)
Dividend-paying stock 3.50% 3.50%
(no appreciation and dividends are taxed at 15%)
Growth stock FV $65,000 FV $140,000
Municipal bond (tax-exempt) 3.20% 3.10%
Alan and Alice should invest in growth stocks since they yield the highest after tax return:
5 years:
FV of growth stocks = $65,000
taxable gain = $65,000 -$50,000 = $15,000 x 15% = $2,250
net gain = $15,000 - $2,250 = $12,750
to determine the yield rate we can use the future value formula:
62,750 = 50,000 x (1 + r)⁵
(1 + r)⁵ = 62,750 / 50,000 = 1.255
⁵√(1 + r)⁵ = ⁵√1.255
1 + r = 1.046
r = 4.6% after tax yield per year
18 years:
FV of growth stocks = $140,000
taxable gain = $140,000 -$50,000 = $90,000 x 15% = $13,500
net gain = $90,000 - $13,500 = $76,500
to determine the yield rate we can use the future value formula:
126,500 = 50,000 x (1 + r)¹⁸
(1 + r)¹⁸ = 126,500 / 50,000 = 2.53
¹⁸√(1 + r)¹⁸ = ¹⁸√2.53
1 + r = 1.053
r = 5.3% after tax yield per year
