Question

The balance in a savings account at the end of each year is shown below. The year is denoted by n, and the account balance is

denoted by An).

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n

A(n)

1

$110.00

2

$121.00

3

$133.10

4

$146.41

If the bank pays 10% compound interest, what function represents the total amount in the account in year n?

O A(n) = 100(1.1)"

O A(n) = 100n1.1

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O A(n) = 100n (1.1)

A(n) = 100 (1.1 + n)

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Answer 1

A(n) = 100(1.1)^n

Explanation:

Given that :

Account balance = A(n)

Compound interest paid = 10%

We need to obtain the initial amount deposited, that is A(n), when n = 0

In year, n = 1

Account balance, A(n) = $110

Let initial deposit = P

Hence,

Compound interest relation should be ;

A(n) = P(1 + r)^n

Plugging in our values

110 = P(1 + 0.1)^1

110 / P = 1.1^1

110/P = 1.1

110 = 1.1P

P = 110 / 1.1

P = 100

Hence, we can define the amount paid inn n years by substuting the value of P into the compound interest formula :

A(n) = 100(1 + 0.1)^n

A(n) = 100(1.1)^n