Final answer:
The problem is solved by first calculating the future value of a $4,000 lump sum payment to be received in 3 years and compounding it for 19 years at a 3.4% interest rate. Then, calculate the future value of 10 annual payments of $11,000 each, starting 4 years from now. The results are combined to determine the total future value in the account in 22 years.
Step-by-step explanation:
The question involves calculating the future value of money, incorporating the concepts of a lump sum payment and an annuity with interest compounding annually. First, we break the problem into two parts. The initial $4,000 payment will compound for 19 years (22 years minus the 3 years until you receive it) at a 3.4% interest rate. Then, we calculate the future value of the annuity, which consists of 10 annual payments of $11,000 starting 4 years from now. These payments will occur annually for 10 years, and the last payment will compound for 8 years until the 22-year mark.
To calculate the future value of the $4,000 lump sum, the formula used is FV = PV * (1 + r)ⁿ, where PV is the present value, r is the annual interest rate, and n is the number of compounding periods. For the annuity, we use the future value of an annuity formula. After determining both future values, we sum them to find the total amount in the account in 22 years. Remember to round the final result to the nearest whole dollar.