Question

You are given $1,000 today and intend placing this in a savings account which will earn interest at 12 percent. You also decide to save and add $1,000 to the account at the end of each of the next four years. How much will you have in the savings account by the end of year five?

Answer 1

To determine the total amount in the savings account by the end of year five, one would calculate the future value of the initial $1,000 using the single sum future value formula and then sum the future values of each subsequent $1,000 end of year annuity payments using the annuity formula.

Step-by-step explanation:

The question asks for the final amount in a savings account after depositing $1,000 initially and then adding $1,000 at the end of each of the next four years, with interest compounded at 12 percent annually. To calculate this, we use the future value of an annuity formula combined with the future value of a single sum.

For the first $1,000 deposited today, we use the single sum future value formula: Future Value = Present Value x (1 + interest rate)^number of periods. Therefore, the future value of the initial $1,000 after five years is $1,000 x (1 + 0.12)^5.

For the subsequent deposits, we would use the annuity formula: Future Value of Annuity = Payment x [((1 + interest rate)^number of periods - 1) / interest rate].

Each of the annual $1,000 deposits is made at the end of the year, so each will have compounded for one year less than the previous deposit. The first deposit will compound for four years, the second for three, and so on until the final deposit, which does not compound as it is made at the end of the fifth year.

Adding the future values of all these deposits together will give the total amount in the savings account at the end of year five.