Investment compound interest formula to compare tax effective Superannuation, Investment Bonds and Direct

General compound interest formula:
P = Principal

i = interest rate

n = number of compound periods

Compound Interest (above Principal) = P * ((1 + i)^n – 1)

Rule of 72:
A simple way to calculate compound interest is the rule of 72. It is used for estimating an investment's doubling time. The number 72 is divided by the interest percentage per period (usually years) to obtain the approximate number of periods required for doubling.

The chart below compares the numbers given by the Rule of 72 and the actual number of years it takes an investment to double:

Rate of Return	Rule of 72	Actual # of Years	Difference (#) of Years
2%	36.0	35	1.0
3%	24.0	23.45	0.6
5%	14.4	14.21	0.2
7%	10.3	10.24	0.0
9%	8.0	8.04	0.0
12%	6.0	6.12	0.1
25%	2.9	3.11	0.2
50%	1.4	1.71	0.3
72%	1.0	1.28	0.3
100%	0.7	1	0.3

Below is a comparison of investments in the same Vanguard ETF: Superannuation, Investment Bonds and Direct:

Superannuation:
Assumptions:

• 2.5% dividends
• 6.5% annual capital growth
• 0.5% management fee
• 15% tax on Superannuation
• 10 year investment

(1 + (0.025 – 0.005 * 0.85))^10 -> 22.8% after-tax dividends
((1.065^10)-1)*0.9 -> 78.9% after-tax capital gains
Total gain after 10 years: 101.7%

Investment Bond (LifePlan allows Vanguard ETFs):

Assumptions:

• 2.5% dividends
• 6.5% capital growth
• 0.6% management fee
• 10 year investment
• if you hold the bond for more than 10 years, it is tax-paid and you pay no CGT on sell
• you can add up to 125% of your previous year's contribution, without resetting the 10 year limit
• income tax is charged at 30% (company rate tax)

(1 + ((0.025-0.006) * 0.7))^10 -> 14.1% after-tax dividends
(1.065^10)-1 -> 87.7% after-tax capital gains (no tax)
Total gain after 10 years: 101.8%

Direct Vanguard Investment 32.5% marginal tax rate:

Assumptions:

• 2.5% dividends
• 6.5% capital growth
• 0.14% management fee
• 10 year investment
• income tax is charged at 32.5% marginal tax rate
• 50% CGT discount rule for assets held at least 1 year

(1 + ((0.025-0.0014) * 0.675))^10 -> 17.1% after-tax dividends
((1.065^10)-1)*0.8375-> 73.4% after-tax capital gains (discount of 50%)
Total gain after 10 years: 90.5%

Direct Vanguard Investment 37% marginal tax rate:

Assumptions:

• 2.5% dividends
• 6.5% capital growth
• 0.14% management fee
• 10 year investment
• income tax is charged at 37% marginal tax rate
• 50% CGT discount rule for assets held at least 1 year

(1 + ((0.025-0.0014) * 0.63))^10 -> 15.9% after-tax dividends
((1.065^10)-1)*0.815 -> 71.4% after-tax capital gains (discount of 50%)
Total gain after 10 years: 87.3%

Direct Vanguard Investment 45% marginal tax rate:

Assumptions:

• 2.5% dividends
• 6.5% capital growth
• 0.14% management fee
• 10 year investment
• income tax is charged at 45% marginal tax rate
• 50% CGT discount rule for assets held at least 1 year

(1 + ((0.025-0.0014) * 0.55))^10 -> 13.7% after-tax dividends
((1.065^10)-1)*0.775 -> 67.9% after-tax capital gains (discount of 50%)
Total gain after 10 years: 81.6%

From above looks like investment bonds can even beat superannuation in tax efficiency.

Update 12/5/2019: Investment bonds do pay CGT on growth:
https://www.smh.com.au/money/investing/insurance-bonds-are-not-what-theyre-cracked-up-to-be-20180118-h0kbn5.html
I had some doubts whether investment bonds like LifePlan pay CGT without discount (after holding asset for over 12 months) so I called Australian Unity the company offering LifePlan investment bonds to ask whether there they pay any CGT on growth and they suggested that they do not pay any tax on growth just on dividends.

Product providers can dance around the language but they can't dance around the return figures.

Lifeplan Investment Bd-Vanguard IntShIdx LIF0134AU has a return net of fees and taxes of 9.44% p.a. over the last 5 years. This is a total growth return as the structure doesn't pay out any income.

This fund invests in Vanguard International Shares Index VAN0003AU and over the same period this investment net of fees, gross of tax has returned 13.67% p.a. which is made up of 4.41% income and 8.71%. This income component would include some distributions of gains (that are taxed favourably) but let's assume a worst case scenario and that 100% of the 4.41% income less 0.6% admin fee is taxed at 30% leaving you with 2.67%. If the growth isn't taxed, this should leave you with a return around 11.38% instead of the actual 9.44%.