Compound interest question anyone? (1 Viewer)

[mysticwater]

I think its compound interest but how would you answer this?

Maria opens a saver account which pays interest at the rate of 0.4% per month compounded monthly at the end of each month. She decides to deposit $400 unto the account on the first of each month. She makes her first deposit on 1st Jan 07 and her last on 1st July 09. Maria withdraws the entire amount including interest immediately after her final interest payment on 31st July09.

1)How much did she deposit into her saver account?

2)How much did Maria withdraw from her account on 31st July 09?

3)If Maria decides to deposit $10,000 into a different account which offers interest at the rate of 5% p.a compounded quarterly for 2 yrs, how much will she receive at the end of investment?

 

[hscishard]

I think there are 31 periods.
12,400
13,226.29
24,271.15

2nd one uses GPs
3rd is money in ii) + 10000(1.0125)^8

 

[Deathless]

I think this is the Compound interest formula.

Using this, just extend it with each period till you see a pattern and use the GP series pattern where R < 1

I think it is:


Just follow that and fit it to your question, I think. I haven't revised on sums and sequences yet, so I'm not sure. But from memory, I think what I've said is right.

 

[hscishard]

r in this case should be 1.004

 

[sazlik]

I got the same answers as hscishard:

1. There are 31 terms (months). You find this just by finding the amount of time between January 2007 and July 2009. (12 months + 12 months + 7 months)

Each term, she deposits $400--making a total of $400 x 31 = $12 400 deposited into her account.


2. This is a superannuation question.

The first $400 will be invested for 31 terms and will amount to $400 x 1.004^31.
The second $400 will be invested for 30 terms and will amount to $400 x 1.004^30.
And so on until the last $400 which will be invested for 1 term and will amount to $400 x 1.004.

At the end of the 31 terms (when she takes the money out of the account), the investment will be worth:
$400(1.004^31 + 1.004^30 + 1.004^29 + ... + 1.004)
= $400(1.004 + 1.004^2 + 1.004^3 ... + 1.004^31)
= $400 x 1.004(1.004^31 - 1)/(1.004 - 1) [using the geometric sum formula]
= $13 226.29 to the nearest cent.


3. I interpreted this question slightly differently to hscishard--I didn't add on the amount from 2 because it didn't seem like the question was asking for the sum of both investments. But this one is just the compound interest formula:

5% p.a. compounded quarterly is 1.25% quarterly; and there are 2 years, so there are 8 quarters.

So, after 8 quarters, the amount is 10000(1.0125)^8 = $11 044.86 to the nearest cent.


I hope that's a bit helpful!

 

[hscishard]

I think you'lll still get the marks if you did one extra step. As long as you underline anything as answer. It's like writing 1+1=2 in your exam, you won't lose marks for that.