Help me calculate if this money is safe against the inflation

Question

My friend invested in a 10 year insurance-investment plan where he pays a yearly premium of 30,000 for 5 years and keeps the money for another 5 years (He cannot withdraw the money for this period). After 10 years, if he receives a total sum of 250,000 - was his money protected against the inflation, considering the average inflation of the country is 6%?

Here's how I tried to calculate:

Interest = (P*R*T)/100
Interest in this case is lump sum received - invested value
i.e 250,000 - 150,000 = 100,000
100000 = (150000 * R * 10)/100
R = 6.66%

So, he beats the inflation by 0.66%?

I have a feeling that my logic is horribly flawed which is why I'm here. Because of the compounding nature of inflation should I even use the formula for the simple interest? Or should it be compound interest's?

Answer 1

If you mean, Is he doing better than inflation?, then yes.

Both inflation and interest compound, so you should consider this in the calculation. The easiest way to do this is probably with a spreadsheet. There are formulas but when you have multiple deposits over time then you stop depositing but it continues to grow, it gets complicated.

So here's what I did. I created a spreadsheet with a column for "Add". In this column I put 30000 for the first 5 rows and then 0 after that. Then I have a column for "total" with the formula "=(e3+b4)*1.07", where column E is the total column and column B is the Add column. 1.07 would represent a 7% growth rate in the value of the account. My intent was to play with numbers until it came out to 260000 after 10 years, but in fact my first guess, 7%, came out to 258,909, which is very close, so I just left it at that.

Note the way I set up the formula I'm calculating based on the assumption that he deposits 30000 the first day of each year. If the 30000 is spread over the year, the growth is actually a little better. But I don't know whether the deposits are monthly or quarterly or what so I just used the simplest formula.

So he's getting a return on his money of a little over 7%. If inflation is 6%, then he's beating that by about 1%. Whether this is a good investment depends on his risk tolerance and what other investments are available.

Answer 2

You are using the term 'protected against inflation'. When I hear that, it implies to me that the intent is to ensure that rising inflation does not have a negative impact. Since this is a sales pitch from a whole-life insurance product, it doesn't surprise me that they are implying more protection than they actually offer.

In short - what happens if inflation is 8% next year, and every year after? Well, then the interest earned would be less than the inflation. And if inflation drops to 4%, then this product will do a lot better than inflation. This product does not change the return provided based on annual inflation amounts, so it has no ability to hedge against that risk.

Edit to include calcs now that we understand the product you're looking at:

First, observe that India's current fixed rate of return on government bonds appears to be 7.29% for a 10 year term [http://www.worldgovernmentbonds.com/country/india/#:~:text=The%20India%2010Y%20Government%20Bond,last%20modification%20in%20September%202022).] We can consider that the 'base level' comparison of whether this product is a net benefit to you or not.

The Net Present Value of having to give up 30k per year for the next 5 years [starting today, and then every 12 months], is 130,954. The math to show this is:

  30k / (1 + 7.29%)^0 = 30,000 [The value of 30k today, is 30k]
+ 30k / (1 + 7.29%)^1 = 27,961 [30k given up in 12 months, is worth 27k]
+ 30k / (1 + 7.29%)^2 = 26,061 [30k given up in 24 months is worth 26k, etc.]
+ 30k / (1 + 7.29%)^3 = 24,290
+ 30k / (1 + 7.29%)^4 = 22,640

= 130,954

This means that from a finance perspective, using the 7.29% comparative government rate to determine the time value of money, giving $30k per year for 5 years is the same as giving 130,954 today.

Now we can compare that with the value of receiving 250k at the end of 10 years [I believe per your wording the funds would be receivable at the end of 10 years, not in the beginning of the 10th year], which is $123,693, calculated as:

250k / (1 + 7.29%) ^ 10

Therefore, the present value of the amount to be received in 10 years is worth less than the value of the amounts being paid over the first 5 years!

We can see that instead of buying this product, your friend could simply purchase a government bond to receive a higher higher rate of interest. Whether that would lose other benefits I don't know, but it is easy to see that this doesn't seem to be the best value for money.

Answer 3

TL;DR his money are not safe at all

No reasonable investment schema can guarantee you profit without risk.

If the deal guarantees fixed profit, it means either it's a scam, or it's a very risky investment schema. Because if markets go down, the only way you can win the guaranteed profit is to invest in very risky instruments. Either you win, pay the guaranteed sum and get anything above as your bonus, or you loose anything, file insolvency, and probably keep his management fee anyway. You've lost only your customer's money.

Answer 4

Laying out an example calculation, with interest say 5% p.a. The first 5 years are

d = 30000
r = 0.05
a = d
a = a (1 + r) + d
a = a (1 + r) + d
a = a (1 + r) + d
a = a (1 + r) + d
a = a (1 + r) = 174057.38

Equivalently

n = 5
a = (d (1 + r) ((1 + r)^n - 1))/r = 174057.38

Subsequent 5 years

m = 5
a = a (1 + r)^m = 222146.23

Putting both parts together

So in full

d = 30000
r = 0.05
n = 5
m = 5
a = (d (1 + r)^(1 + m) ((1 + r)^n - 1))/r = 222146.23

In reverse, with r as unknown, solving the above with guesses for r finds r = 0.05 as expected.

Likewise, solving (d (1 + r)^(1 + m) ((1 + r)^n - 1))/r = 250000

finds r = 0.0654017 beating inflation by an apparent 0.54%

However, applying interest and discounting for inflation simultaneously

i = 0.06
(1 + r)/(1 + i) - 1 = 0.51% p.a.

Also, for example, 30000 after 10 years at these rates

30000 ((1 + r)/(1 + i))^10 = 31564.34 present value