Return on investment & Interest rate comparisons

Question

For the question to make sense I need to provide some context on the products available, below is an example of how banks make money for just two products.

We have infrastructure bonds at 12% per/year interest paid twice a year and principal at the end of the term.

e.g. on $1,000 Investment in January I receive $60 in June and $60 in December plus my $1,000 back. So I made $120 on interest

We have financing of another near risk free asset (Insurance premium Financing) at 6% for 10 months paid monthly. (principal and interest split into 10 equal instalments.)

e.g. for a $1,000 investment the interest is $60. The monthly instalments will be (principal +interest) / period

What would be the the best way to compare what has a better effect on my bottomline at end of 12 months? Because it's not as simple as $120 v $60 interest because in the second example I'm getting back my principal monthly which must count for something. As the principal I claim back can go out and be lent again.

My working outs suggest in the first twelve month if I continue to lend USD 1000 every month net of my principal returned it works out to 13.2% because after the first 4 month no new principal is required to actually charge interest. As my monthly instalments of principal are equal to $1000 dollars.

Answer 1

To compare investment strategies, you need settle out exactly what those strategies are.

I'm getting back my principal monthly which must count for something. As the principal I claim back can go out and be lent again.

falls short of establishing a definite strategy. So to fill it out, I am going to assume that for the Insurance investment, at the end of each month, $6\%$ of the amount that has been invested in the last 10 months is kept as your benefit, while the remaining monthly installment is considered principle to be put back in as an additional purchase (I'll pretend that any size investment at any time is allowed, and monetary amounts can include fractions of a cent).

So after the first month, your original $\$1000$ investment returns $\$106$. You keep $\$6$ and use the remaining $\$100$ to an additional purchase. The next month, you are paid $\$110$ of returned principle, which you roll back in, and $\$6.60$ as interest that you keep. Etc. If you keep doing this, your total investment will quick rise in the first ten months, then drop significantly as the final payout on the original $\$1000$ investment passes. But it will immediately start rising again and spend several months oscillating before converging on a constant $\$1818.8181818... = \dfrac{\$20000}{11}$. In the first year, you will collect about $\$115.11$, while the second year will do better at $\$134.24$, and eventually, it will settle down to a constant $\$130.91$ a year.

So the long term value of this investment strategy is $\$130.91$ per year, whereas for the bond it is only $\$120$ per year.

FYI - I developed the numbers on a spreadsheet. It is possible to find a formula for the Insurance investment, telling you exactly what the earnings are each month without having to track and sum them individually, but that formula would involve powers of two real and eight complex numbers, and would actually be the harder method of calculation.