Suppose you deposit $1,000 today in an account that pays 5% interest at the end of each year. If you withdraw one half of the year's interest at the end of each year, what is the balance in
Your account after your third withdrawal? Round your answer to the nearest dollar.
A)$1,050
B)$1,077
C)$1,000
D)$1,216

Question

Quizplus · Accepted Answer

After one year: 
Balance = $1,000 + 5% of $1,000 = $1,050 
Withdrawal = 1/2 * 5% of $1,000 = $25 
Remaining balance= $1,025

After the second year: 
Balance = $1,025 + 5% of $1,025 = $1,076.25 
Withdrawal = 1/2 * 5% of $1,025 = $25.62.5 
Remaining balance= $1,050.63

After the third year: 
Balance = $1,050.63 + 5% of $1,050.63 = $1,103.16 
Withdrawal = 1/2 * 5% of $1,050.63 = $26.27 
Remaining balance= $1,076.89

Rounding to the nearest dollar gives a balance of $1,077. Therefore, the best choice is B. After one year, the interest earned is $1,000 x 0.05 = $50. If you withdraw half of this, you take out $25, leaving your balance at the end of year one at $1,025.

After two years, the interest earned is $1,025 x 0.05 = $51.25. If you withdraw half of this, you take out $25.63, leaving your balance at the end of year two at $1,051.63.

After three years, the interest earned is $1,051.63 x 0.05 = $52.58. If you withdraw half of this, you take out $26.29, leaving your balance at the end of year three at $1,077.29. Therefore, the best choice is B, with the balance being $1,077.

Suppose You Deposit $1,000 Today in an Account That Pays