Write a sequence that represents the amount of money that will accumulate if the principal is P and the interest rate per year is r.Interest is compounded monthly. Determine tn. What...

Write a sequence that represents the amount of money that will accumulate if the principal is P and the interest rate per year is r.

Interest is compounded monthly. Determine tn. What does n represent?

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embizze's profile pic

embizze | High School Teacher | (Level 1) Educator Emeritus

Posted on

We are given an initial principal of `P` , and interest rate `r` , and that the account is compounded monthly.

The compound interest formula is:

`A=P(1+r/n)^(nt)` ; with n=12 we have `A=P(1+r/12)^(12t)`

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The sequence generated will be:

`T_0=P`

`T_1=P(1+r/12)^12`

`T_2=P(1+r/12)^24`

`T_3=P(1+r/12)^(36)`

`T_n=P(1+r/12)^(12n)`  where `n` is the number of years after the initial deposit.

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Sources:
sciencesolve's profile pic

sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted on

You should write the formula of compound interest such that:

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

Notice that the problem provides the information that the interest is compounded monthly, hence, you should substitute 12 for n in equation that gives the compound interest such that:

`A = P(1 + r/12)^(12t)`

Hence, using the formula of compound interest `A = P(1 + r/12)^(12t)`  yields that `nt = 12 t`  and `n = 12`  represents the number of times the interest is compounded over an year.

Sources:

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