financial maths regular investments (1 Viewer)

[totallybord]

Hi,
Could someone show the working out and explanations for this question:
A person pays $2000 into an investmnet fund every 6 months and it earns interest at a rate of 6% p.a, compounded monthly. HOw much is the fund worth at the end of 10 years?
Answer: $55 586.38

Thank you!

 

[Drongoski]

Hi,
Could someone show the working out and explanations for this question:
A person pays $2000 into an investmnet fund every 6 months and it earns interest at a rate of 6% p.a, compounded monthly. HOw much is the fund worth at the end of 10 years?
Answer: $55 586.38

Thank you!

Hey - how come you have a Rep Power of 6 getting mainly help and I've got the same after over 2 years of providing help??


The Final Amount A




Will show workings later.

 

[powlmao]

Hey - how come you have a Rep Power of 6 getting mainly help and I've got the same after over 2 years of providing help??

It is the weird life of BOS

 

[powlmao]

Hi,
Could someone show the working out and explanations for this question:
A person pays $2000 into an investmnet fund every 6 months and it earns interest at a rate of 6% p.a, compounded monthly. HOw much is the fund worth at the end of 10 years?
Answer: $55 586.38

Thank you!

I can get your question but what does the account start with??

Does it originally start with 2k? or?

 

[maths lover]

Does it originally start with 2k? or?

obviously!

 

[Drongoski]

It is the weird life of BOS

Question a bit ambiguous - did not make clear if each $2000 is invested at BEGINNING of each 6-month period or at the END. Turns out it is at the beginning (and this makes more sense) Now 6% p.a. is equivalent to 0.5% per month. So question is equivalent to an EFFECTIVE interest rate every 6-month period of (1 + 0.005)⁶ = 1.03037759 - i.e. an equivalent 6-monthly interest rate of 3.03037759%. Let R = 1 + 0.03037759 = 1.03037759

So:

1st $2000 is compounded for 20 compounding periods so that at the end of 10 yrs this amount A-1 = $2000 (R^20 )

Therefore:

A-1 = $2000 x R^20
A-2 = $2000 x R^19

.
.
.
A-19 = $2000 x R^2
A-20 = $2000 x R^1

Therefore total amount = A-1 + A-2 + . . . + A-20 = $2000 x R x (R^20 - 1)/[R - 1]

 

[kooliskool]

Question a bit ambiguous - did not make clear if each $2000 is invested at BEGINNING of each 6-month period or at the END.

Erm, isn't it obvious it should be at the beginning? I mean, what is the point of investing at the end........ you get no interest for 1 period and start to only accumulate interest next period? It's like superannuation funds, if you have the money now, why do you keep it til the end to save it for interest.

You could also look at it at the end point, why would you save some money into an account and get it out straight away (without getting interest).

So to me, the only way that makes sense is always superannuation => save it at the beginning.

It's different to loan, you take out a loan, so you pay at the end of the period, otherwise why bother take out the loan, take out less then if you are paying it back straight away.

 

[Gigacube]

Hey - how come you have a Rep Power of 6 getting mainly help and I've got the same after over 2 years of providing help??

Make smart-ass comments and you'll get more rep. That's how things work on BOS unfortunately. You don't get credit you deserve for helping others.

 

[enveloped]

Hey,
I found this in the Cambridge book which actually came before the question from the OP and was a bit confused...
A finance company has agreed to pay a retired couple a pension of $15 000 per year for the next twnety years, indexed to inflation which is 3.5%.
How much will the company have paid the couple at the end of twenty years?
Immediately after the tenth annual pension payment is made, the finance company increases the indexed rate of 4% per annum to match thte increased inflation rate. Given these new conditions, how much will the company have paid the couple at the end of twenty years?

The answers are $424 195.23 and $431 235.13.
Please explain the steps! Thank you=]