Question

You can save $2,000 per year for the next five years, at the start of each year, in an account earning 8 percent per year. How much will you have at the end of the fifth year if you make the first deposit today?

Answer 1

By saving $2,000 at the beginning of each year with an 8 percent interest rate, you will have approximately $12,671.21 at the end of the fifth year due to compound interest.

Step-by-step explanation:

Understanding Compound Interest

To calculate how much you will have at the end of the fifth year after saving $2,000 per year at an interest rate of 8 percent, we will use the future value formula for an annuity due. An annuity due is a series of equal payments made at the beginning of each period. In this case, your payments are made at the beginning of each year (annuity due), which means that each payment also earns interest for the year.

By using the future value formula for an annuity due: FV = P × 【((1 + r)n - 1) / r)】 × (1 + r), where:

• P = periodic payment ($2,000)
• r = interest rate per period (0.08)
• n = number of periods (5 years)

We calculate the future value (FV) as follows:

FV = 2000 × 【((1 + 0.08)5 - 1) / 0.08】 × (1 + 0.08)

First, calculate the part within the brackets:

(1 + 0.08)5 - 1 = (1.08)5 - 1 ≈ 0.4693

Now divide by the interest rate, r:

0.4693 / 0.08 ≈ 5.8663

Then, multiply by the periodic payment, P:

2000 × 5.8663 ≈ $11,732.6

Finally, multiply by 1 + r to account for the annuity due:

$11,732.6 × (1 + 0.08) ≈ $12,671.21

Therefore, at the end of the fifth year, you will have approximately $12,671.21.