# Write a sequence that represents the amount of money that will accumulate if $10 000 is invested at 8% per year, compounded quarterly.Determine tn. What does n represent?

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### 2 Answers

We are given the original principal of $10,000; the interest rate of 8%, and that the account is compounded quarterly. Using the compound interest rate formula:

`A=P(1+r/n)^(nt)` we have `A=10000(1+(.08)/(4))^(4t)` or `10000(1.02)^(4t)`

Here `t` is the number of years after the initial deposit.

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**The sequence generated is:**

**`T_0=10,000` **

**`T_1=10824` **

**`T_2=11717` **

**`T_3=12682` **

**`T_n=10000(1.02)^(4n)` where `n` represents the number of years after the initial deposit.**

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There can be a lot of confusion since we are using t and n in two different ways. It would be better to use different variables to avoid the confusion.

**Sources:**

You should remember the formula of compound interest such that:

`A = P(1 + r/n)^(nt)`

The problem provides the following informations: P = 10 000 (amount invested), `r = 8/100 = 0.08` (annual rate) , n = 4 (number of time the interest is compound/year).

`A= 10 000(1 + 0.08/4)^(4t)`

`A= 10 000(1.02)^(4t)`

**Hence, evaluating the amount of money acumulated after a number of years, yields `A = 10 000(1.02)^(4t)` , where n = 4 represents the number of time the interest is compound/year and `tn = 4t` . **

**Sources:**