# Help me calculate if this money is safe against the inflation

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?

• How safe is the money? Is it in a bank with FDIC or similar insurance? Is it invested in some mystery investment? Commented Nov 10, 2022 at 13:25
• With compound interests, depending on when the interest is added (at the start or end of a year, or more often), I calculate that as approximately a 6.54% annual rate. Commented Nov 10, 2022 at 13:53
• @Flux : I believe that data is valid only for the United States and not for other countries. Commented Nov 10, 2022 at 15:49
• I would be seriously turned off by a sales pitch that explained itself as poorly as these guys appear to have done. It is a massive warning flag that an institution would try to gloss over the mechanics of how things work, to people who are not familiar with the terms. In short, this appears to be a classic sales pitch for an overly aggressive high-commission product, which 'insurance investments' definitely are. Doesn't mean it's a scam, but you should understand that there's a whole world of investing out there which doesn't take a 10%+ haircut off the top for commission. Commented Nov 11, 2022 at 13:40
• Does this answer your question? Whole Life Insurance As Inflation-Protected Liquid Cash Savings (Emergency Fund) Commented Nov 11, 2022 at 13:48

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.

• Two things: (1) I think the value of the answer would increase if you were more explicit about the actual math behind comparing the value of the inflows and outflows [referring to the present value of the outflows over 5 years at a 6% inflation rate vs the PV of the inflow in 10 years at a 6%, which is the simplest method to show whether the rate evenly breaks above or below the comparative], and also I think some discussion of the implication for hedging against inflation risk should be discussed, although I may be reading too much into this. Commented Nov 10, 2022 at 17:10
• @Grade'Eh'Bacon It would certainly be valid to calculate discounted present value allowing for inflation, or to calculate what the final balance would be if it was just enough to balance inflation. Those would be different approaches to answering the question. I think the conclusion would be essentially the same. If you prefer that approach ... write your own answer doing it that way. :-)
– Jay
Commented Nov 11, 2022 at 4:53

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.

• This is not an assignment. My friend and I were discussing the investment options we know of and I was a bit skeptical when he mentioned that his investment scheme performs better than the inflation, gives him tax exemptions and has zero risk (Refer my comments on the post). The wording seems off because neither me nor my friend has any academic or work experience in finance. Commented Nov 10, 2022 at 17:29
• If its for real, it sure sounds a lot as scam or pyramid scheme. I would be careful.
– JIV
Commented Nov 11, 2022 at 8:27
• @7_R3X Okay I understand why it sounded like a homework problem in your wording - because the information provided to your friend in the sales pitch was carefully crafted to be simplistically optimistic, like what you would see in a textbook. Again - you are using the term "zero risk" [I assume this wording filtered through the sales pitch], which can mean a few different things, but what it does not mean, is that it is necessarily a good investment. 'Zero risk' in finance simply means "you know exactly what you will get, no variance". Commented Nov 11, 2022 at 13:43
• I have no knowledge of this product, but be careful that one of the biggest downsides of such a scheme is often that the lock-in period is geared so that if you need an early withdrawal, you have to walk away without the return at the end of the day. Commissions are often also insanely high. It is unclear whether there is anything special about this product at all, except that it has an interest rate over 10 years that is higher than what you could get on a short term bank product. Even mentioning the word 'inflation' seems to be just selling tactics reflecting the ever-present 2022 concern. Commented Nov 11, 2022 at 13:45

## 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.

• This is a reasonably standard life assurance scheme which companies have been succesfully doing for hundreds of years, The guaranteed amounts will be paid out - but they will be less than you can get elsewhere - for this policy you are hoping that the insurance company has good investments to add the bonus. ie this is low risk but low reward. Commented Nov 11, 2022 at 11:14

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

$\sum_{k=1}^{n}d(1+r)^{k}=\frac{d(1+r)((1+r)^{n}-1)}{r}$

``````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

$\frac{d(1+r)((1+r)^{n}-1)}{r}(1+r)^{m}=\frac{d(1+r)^{1+m}((1+r)^{n}-1)}{r}$

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
``````