Question

To save for a car when he turns 18, Pascale deposited $500 each year into a savings account with a 7.5% interest rate compounded annually. Year Beginning Balance Interest Earned Ending Balance 1 $500.00 $37.50 $537.50 2 $1,037.50 $77.81 $1,115.31 3 $1,615.31 $121.15 $1,736.46 4 $2,236.46 $167.73 $2,404.19 5 Using the formula A = P (1 + r) Superscript t, what is the value of the account at the end of the fifth year? $3,071.92 $3,122.00 $3,851.77 $4,140.65

Answer 1

The value of Pascale's savings account at the end of the fifth year, with a 7.5% interest rate compounded annually and an additional $500 deposited each year, is approximately $3,122.00.

Step-by-step explanation:

To calculate the value of Pascale's account at the end of the fifth year, we must use the compound interest formula which is A = P (1 + r)^t, where:

• 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 (decimal).
• t is the time the money is invested for in years.

However, since Pascale deposits an additional $500 at the beginning of each year, the calculation is more complex than a single application of the formula. Our calculation should reflect the compound interest earned on each individual $500 deposit, not just the initial deposit.

Let's calculate the value at the end of year 5 step by step, adding $500 at the beginning of each year:

1. The balance at the beginning of year 5 is $2,404.19.
2. Pascale deposits an additional $500 at the start of year 5, making the new starting balance $2,904.19.
3. Now apply the compound interest formula for year 5: A = $2,904.19 * (1 + 0.075)^1 (since interest is compounded annually).
4. This equals: A = $2,904.19 * 1.075 = $3,122.00 (approximately).

Therefore, the value of the account at the end of the fifth year is approximately $3,122.00.