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March 7th, 2017, 04:17 PM   #1
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Representing as a Function problems

Hello! I am looking for explanations for the following 2 problems:

1.) Fresh Bank offers a savings scheme that accrues simple interest annually based on an initial deposit of $1000. If S(t) represents the money in the account at the end of t years and S(7) = 1350, write a function that could be used to determine the amount of money in the account over time.


2.) Campus Ban offers savings account that accrues compound interest annually at a rate of 3%

What is the initial amount needed in this account so that it will have the same amount of money at the end of 15 years?


Thank you in advance.
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March 7th, 2017, 06:43 PM   #2
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Assuming annual accrual of interest at rate $r$

$V(t) = 1000(1+r)^t,~\text{t in years.}$

$V(7) = 1350 = 1000(1+r)^7$

$1.35 = (1+r)^7$

$(1.35)^{1/7} = 1+r$

$r = (1.35)^{1/7}-1 \approx 0.0438$

$V(t) = 1000(1.0438)^t$
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March 7th, 2017, 06:46 PM   #3
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Quote:
Originally Posted by IvyMath View Post
2.) Campus Bank offers savings account that accrues compound interest annually at a rate of 3%

What is the initial amount needed in this account so that it will have the same amount of money at the end of 15 years?
You don't mention making withdrawals anywhere.

If you want to have the same amount of money in 15 yrs as you start with then you have to start with 0.

Somehow I don't think that's what the problem means. Could you make it clearer?
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March 8th, 2017, 06:16 AM   #4
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Quote:
Originally Posted by romsek View Post
You don't mention making withdrawals anywhere.

If you want to have the same amount of money in 15 yrs as you start with then you have to start with 0.

Somehow I don't think that's what the problem means. Could you make it clearer?
Hello and thank you!

The problem originally said :
Part B:

Alternatively, Campus Bank offers savings account that accrues compound interest annually at a rate of 3%

What is the initial amount needed in this account so that it will have the same amount of money at the end of 15 years?

So we should assume that its related to problem A. I think the question is asking what amount of money you need in order to get back the investment you put in 15 years.

Sorry if I didn't make it clear enough last time!
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March 8th, 2017, 01:34 PM   #5
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(1). S(t) = 1000 + 50t

(2). The target number of dollars is 1000 + 50*15 = 1750.
If you invest \$1123.25 at 3% (rounded) annual compound interest, it will have grown to \$1750.01 after 15 years.
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