Final answer:
To calculate the future value of the deposits, we separately computed the future value of $500 over 4 years and $1,000 over 1 year using the formula Principal(1 + interest rate)^time, resulting in a total of $1,657.75 by the end of year 4.
Step-by-step explanation:
To compute the future value of two separate deposits using a 5 percent interest rate, we separate the calculations based on the timing of each deposit.
Calculating the Future Value for the First Deposit ($500)
For the $500 deposit made in year 1 and held until the end of year 4:
Future Value = Principal × (1 + interest rate)time
Future Value = $500 × (1 + 0.05)⁴
Future Value = $500 × (1.21550625)
Future Value = $607.75
Calculating the Future Value for the Second Deposit ($1000)
For the $1,000 deposit made at the end of year 3 and held until the end of year 4:
Future Value = Principal × (1 + interest rate)time
Future Value = $1,000 × (1 + 0.05)¹
Future Value = $1,000 × (1.05)
Future Value = $1,050
Combining Both Deposits
The total future value at the end of year 4 is:
Total Future Value = Future Value of First Deposit + Future Value of Second Deposit
Total Future Value = $607.75 + $1,050
Total Future Value = $1,657.75