Your employer has agreed to place year-end deposits of $1,000,$2,000 and $3,000 into your retirement account.The $1,000 deposit will be one year from today,the $2,000 deposit two years from today,and the $3,000 deposit three years from today.If your account earns 5% per year,how much money will you have in the account at the end of year three when the last deposit is made?
A)$5,357.95
B)$6,000
C)$6,202.50
D)$6,727.88

Question

Quizplus · Accepted Answer

To calculate the future value of these deposits, we use the formula for the future value of a single sum, which is $FV = PV(1 + r)^n$, where $FV$ is the future value, $PV$ is the present value (or deposit), $r$ is the annual interest rate, and $n$ is the number of years until the sum is received.1. For the $1,000 deposit, it will earn interest for 2 years (since it's deposited one year from today and we're looking at the value at the end of year 3):$$FV = 1000(1 + 0.05)^2 = 1000(1.1025) = \$1,102.50$$2. For the $2,000 deposit, it will earn interest for 1 year (since it's deposited two years from today):$$FV = 2000(1 + 0.05)^1 = 2000(1.05) = \$2,100.00$$3. The $3,000 deposit is made at the end of year 3, so it does not earn any interest by the end of year 3:$$FV = 3000(1 + 0.05)^0 = 3000(1) = \$3,000.00$$Adding these amounts together gives the total amount in the account at the end of year 3:$$Total = \$1,102.50 + \$2,100.00 + \$3,000.00 = \$6,202.50$$

Your Employer Has Agreed to Place Year-End Deposits of $1,000,$2,000