Money Investing Problem

[starspeed]

Hi there.
A company has 6 Money Saving Funds A,B,C,D,E and F. It gives yearly compounded interest of 20% which is same of all funds.
I want to invest money amounting 5000 monthly in this company's Fund for 30 years. I have two options to invest it.
(a) Either i invest 5000 monthly for 30 years in Fund A
(b) I divide my money into 5 chunks of 1000 each and invest 1000 each monthly in Funds B,C,D,E and F for same 30 years period.

Now my question is that after 30 years, which Fund scheme will give me more returns, scheme(a) or (b) ?

 

[nasi112]

Before going to (b), let us focus on (a)

assuming your investment of [MATH]$5000[/MATH] will be paid at the end of each month

after [MATH]30[/MATH] years, you will have [MATH]$77199375.97[/MATH] in your account

Can you figure out how did we get this number?

 

[Deleted member 4993]

Hi there.
A company has 6 Money Saving Funds A,B,C,D,E and F. It gives yearly compounded interest of 20% which is same of all funds.
I want to invest money amounting 5000 monthly in this company's Fund for 30 years. I have two options to invest it.
(a) Either i invest 5000 monthly for 30 years in Fund A
(b) I divide my money into 5 chunks of 1000 each and invest 1000 each monthly in Funds B,C,D,E and F for same 30 years period.

Now my question is that after 30 years, which Fund scheme will give me more returns, scheme(a) or (b) ?

Suppose B, C, D, E & F are bunched up and made into a "mutual fund" - call it fund G.

How much money/month are you putting into Fund G?

What will be the expected interest rate of fund G? (remember components of fund G - which are B, C, D, E & F - have the same interest rate)?

How is this different from putting $5000/month in fund A @ the given interest rate?

 

[nasi112]

Suppose B, C, D, E & F are bunched up and made into a "mutual fund" - call it fund G.

How much money/month are you putting into Fund G?

What will be the expected interest rate of fund G? (remember components of fund G - which are B, C, D, E & F - have the same interest rate)?

How is this different from putting $5000/month in fund A @ the given interest rate?

the OP will be surprised by the answer

 

[starspeed]

Before going to (b), let us focus on (a)

assuming your investment of [MATH]$5000[/MATH] will be paid at the end of each month

after [MATH]30[/MATH] years, you will have [MATH]$77199375.97[/MATH] in your account

Can you figure out how did we get this number?

No sir, i am not so sure. Maybe compounded interest.

 

[nasi112]

Now my question is that after 30 years, which Fund scheme will give me more returns, scheme(a) or (b) ?

Answering the above question is fairly easy as Khan explained.

But you need to prove it by calculations.

Show me how will you invest $5000 monthly for 30 years with interest rate of 20% compounded annually? Then, I will correct your formula.

 

[starspeed]

Suppose B, C, D, E & F are bunched up and made into a "mutual fund" - call it fund G.

How much money/month are you putting into Fund G?

What will be the expected interest rate of fund G? (remember components of fund G - which are B, C, D, E & F - have the same interest rate)?

How is this different from putting $5000/month in fund A @ the given interest rate?

You mean to say that the final amount remains the same in two cases?
Actually sir, i want to invest my money in mutual funds. It is said that we need to diversify our portfolio to reduce risks. That's why i want to invest in different funds rather than in a single fund.
I actually had a thing in my mind that if i invest 5000 in a single fund, then at the end of 1st year more interest will be generated on that amount and that amount will become principal for next year and that will earn more interest and so on up to thirty years. On the contrary, on 1000 Rs amount, interest generated will be less and so on and if we add up all 5 of these, maybe the amount will be less.

 

[starspeed]

Now my question is that after 30 years, which Fund scheme will give me more returns, scheme(a) or (b) ?

Answering the above question is fairly easy as Khan explained.

But you need to prove it by calculations.

Show me how will you invest $5000 monthly for 30 years with interest rate of 20% compounded annually? Then, I will correct your formula.

I think the final amount = 5000 ( 1 + 20/100)^30 = 1186881.568998849

 

[jonah2.0]

Beer soaked ramblings follow.

... assuming your investment of [MATH]$5000[/MATH] will be paid at the end of each month

after [MATH]30[/MATH] years, you will have [MATH]$77199375.97[/MATH] in your account

Can you figure out how did we get this number?

I am somehow more inclined to lean on the beginning of the month investment scenario but I guess the end of the month scenario is just as good. I would however be wary of any establishment offering such a high rate of return.

 

[nasi112]

Beer soaked ramblings follow.

I am somehow more inclined to lean on the beginning of the month investment scenario but I guess the end of the month scenario is just as good. I would however be wary of any establishment offering such a high rate of return.

Of course if the annuity is at the beginning of the month, it leads to more profit, but in this question or scenario it doesn't matter where we will start. It is just to be consistent of using the same formula to compare (a) and (b)

 

[nasi112]

I think the final amount = 5000 ( 1 + 20/100)^30 = 1186881.568998849

The above calculations that you have done mean that you will put in your account $5000 only 1 time.

But your question was to put money in the account every month!!

Your question is about annuity. Do you understand what does annuity mean?

 

[starspeed]

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The above calculations that you have done mean that you will put in your account $5000 only 1 time.

But your question was to put money in the account every month!!

Your question is about annuity. Do you understand what does annuity mean?

Ok sir.
So the final amount = 5000*12 ( 1 + 20/100)^30 = 14242578.827986188 ??

 

[nasi112]

If you invest [MATH]5000[/MATH] in [MATH]1[/MATH] account, you will get

[MATH]5000 \cdot \frac{(1 + 0.2)^{30} - 1}{(1 + 0.2)^{\frac{1}{12}} - 1} = 77199375.97[/MATH]
If you invest [MATH]1000[/MATH] in [MATH]1[/MATH] account, you will get

[MATH]1000 \cdot \frac{(1 + 0.2)^{30} - 1}{(1 + 0.2)^{\frac{1}{12}} - 1} = 15439875.19[/MATH]
If you invest [MATH]5000[/MATH] in [MATH]5[/MATH] accounts, each account will have [MATH]1000[/MATH], you will get

[MATH]15439875.19[/MATH] x [MATH]5 = \ ?[/MATH]
Which option gives more profit?

 

[JeffM]

I want to dispel a different misconception. Your example does not explain diversification because you are assuming CERTAIN rates of return on all choices. In other words, risk is zero in that example, and you cannot get less than no risk. So diversification is meaningless in the context of your example.

In reality, very few investments have a certain return. If returns are uncertain, diversification leads to less variation in the expected return of the combined investment.

Moreover, returns as high as 20% p.a. are almost always quite uncertain.