Final answer:
To find the future value of deposits made at an 8 percent interest rate, we calculate the value of each individual deposit by compounding it over the given number of years until year 9. Adding each of these future values together provides the total future value of all deposits made.
Step-by-step explanation:
The question requires computing the future value of deposits made at an 8 percent interest rate over various years. Future value (FV) is calculated using the formula FV = P (1 + r)^n, where P is the principal, r is the annual interest rate, and n is the number of years the money is invested for.
For the deposit made in year 1 ($1,100), the future value in year 9 is calculated as $1,100(1 + 0.08)^(9-1). For year 2 ($3,200), it's $3,200(1 + 0.08)^(9-2), and so on for the other years. Calculating the future value for each deposit:
- Year 1: $1,100(1.08)^(8) = $2,039.57
- Year 2: $3,200(1.08)^(7) = $5,523.84
- Year 3: $2,100(1.08)^(6) = $3,342.15
- Year 4: $6,000(1.08)^(5) = $8,885.72
Adding all the future values together, we get $2,039.57 + $5,523.84 + $3,342.15 + $8,885.72 = $19,791.28. The closest answer from the given options is B) $19,668.67 which suggests a possible minor miscalculation or a rounding difference in the answer choices provided.