# 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?

*print*Print*list*Cite

### 2 Answers

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)`

---------------------------------------------------------------

**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.**

---------------------------------------------------------------

**Sources:**

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:**