Question

If a person spends eight dollars a week on coffee, assume $400 a year. What would be the future value of the amount over nine years if the funds were deposited in the account earning one percent?

Option 1: $4,365.60
Option 2: $4,000.00
Option 3: $3,600.00
Option 4: $4,800.00

Answer 1

To find the future value of $400 a year saved over nine years at a 1% interest rate, we use the future value of an annuity formula. The closest correct option to the calculated future value of approximately $3,645.80 is Option 3: $3,600.00.

Step-by-step explanation:

The question involves calculating the future value of a periodic deposit into a savings account with compound interest. To find the future value of spending $8 per week on coffee, the student assumes $400 is deposited annually into an account that earns 1% interest, compounded annually. Over a period of 9 years, we will use the future value of an annuity formula:
FV = P × { [(1 + r)ˉⁿ - 1] / r }

Where:

• P is the annual deposit ($400)
• r is the annual interest rate (1%, or 0.01)
• n is the number of years (9)

After plugging in the values we get:
FV = $400 × { [(1 + 0.01)ˉ⁹ - 1] / 0.01 }

This calculation will give us the future value of the amount after 9 years, which is approximately $3,645.80. Therefore, the closest option provided to this value is Option 3: $3,600.00.