Final answer:
The total account balance of Janet Taylor Casual Wear at December 31, 2019, after calculating compound interest on the initial balance and additional deposits, will be approximately $107,500, corresponding to answer option d.
Step-by-step explanation:
We will address the question of calculating the future account balance of Janet Taylor Casual Wear, given a starting balance, consistent deposits, and an interest rate of 8%. The account has a starting balance of $75,000 and will have deposits of $4,000 at the end of each of the next three years. The contributions and the starting balance will accrue compound interest.
First, let's calculate the future value of the initial $75,000 over the 3 years:
- Future value = Present value × (1 + interest rate)number of years
- Future value of $75,000 = $75,000 × (1 + 0.08)3 = $75,000 × 1.259712 = $94,478.40
Next, let's calculate the future value of the annuity (the $4,000 deposits at the end of each year). An annuity due to an 8% interest rate would give us the following:
- Year 1 future value = $4,000 × (1 + 0.08)2 = $4,000 × 1.1664 = $4,665.60
- Year 2 future value = $4,000 × (1 + 0.08)1 = $4,000 × 1.08 = $4,320
- Year 3 future value = $4,000 (no interest since it's deposited at the end of the year)
Summing up all the future values of the deposits:
- Total future value of deposits = $4,665.60 + $4,320 + $4,000 = $12,985.60
Finally, the total future value of the account balance on December 31, 2019, will be the sum of the future value of the initial balance plus the total future value of the deposits.
- Total account balance = Future value of $75,000 + total future value of deposits
- Total account balance = $94,478.40 + $12,985.60 = $107,464
The best suitable answer, when rounded to the options provided, is $107,500, which corresponds to answer option d.