Question

A high-interest savings account pays 5.5% interest compounded annually. If $300 is deposited initially and again at the first of

each year, which summation represents the money in the account 10 years after the initial deposit?

Answer 1

The owner's account would have a balance of $4075.05 in 10 years.

Answer 2

`\sum_(n=1)^(10) 316.5 (1.055)^(n-1)`

Explanation:

The amount (A) in a deposit after 1 year is calculated as follows:

A = P*(1 + r)

where:

P is the present value

r is the annual rate (decimal)

After the first year:

A = 300*(1 + 0.055) = $316.5

After the second year, the account will have a new amount of $316.5 due to the new $300 and the interest gained with the previous $316.5:

A = 316.5 + 316.5*(1 + 0.055)

After the third year:

A = 316.5 + [316.5 + 316.5*(1 + 0.055)]*(1 + 0.55)

A = 316.5 + 316.5*(1 + 0.055) + 316.5*(1 + 0.055)^2

After 10 years:

`\sum_(n=1)^(10) 316.5 (1.055)^(n-1)`