Question

Suppose we deposit $2,519 in a savings account earning 2.5% per year, compounded annually. Calculate the value of the account at the end of year 34.

Answer 1

The value of the savings account after 34 years with an initial deposit of $2,519 and an annual interest rate of 2.5%, compounded annually, would be approximately $5,327.37.

Step-by-step explanation:

To calculate the value of the savings account at the end of year 34 with an initial deposit of $2,519 earning 2.5% per year, compounded annually, we use the formula for compound interest: A =
`P(1 + r/n)^((nt))`. Here, A is the amount of money accumulated after n years, including interest, P is the principal amount (the initial amount of money), r is the annual interest rate (in decimal form), n is the number of times the interest is compounded per year, and t is the time the money is invested for in years.

In this case, P = $2,519, r = 0.025 (2.5%), n = 1 (since the interest is compounded annually), and t = 34 years. Substituting these values into the formula, we get:
A =
`2519 (1 + 0.025/1)^((1*34))` =
`2519 (1.025)^(34)`.

Calculating this out, the value of the account after 34 years would be approximately A =
`$2,519(1.025)^(34)` = $5,327.37.