Question

Retreaded Tires plans to save $23,500, $24,500, $26,500, and $28,000 at the end of each year for Years 1 to 4, respectively. If it earns 2.1 percent on its savings, how much will the firm have saved at the end of Year 4?
A. $100,878.30
B. $102,140.20
C. $105,608.11
D. $104,174.00

Answer 1

Answer:

• Option C. $105,608.11

Explanation:

Basis:

• Interest compounded monthly
• rate = 0.021/12 = 0.00175

1. Year 1:

All the figures in dollars.

• Initial balance: 0
• Initial balance + interest = 0
• Deposit at the end of the year: 23,500
• Final balance: 23,500

2. Year 2:

All the figures in dollars.

• Initial balance: 23,500
• Initial balance + interest: 23,500 (1 + 0.00175)¹² = 23,998.28
• Deposit at the end of the year: 24,500
• Final balance: 24,500 + 23,998.28 = 48,498.28

3. Year 3:

All the figures in dollars.

• Initial balance: 48,498.28
• Initial balance + interest: 48,498.28(1 + 0.00175)¹² = 49,526.60
• Deposit at the end of the year: 26,500
• Final balance: 26,500 + 49,526.60 = 76,026.60

4. Year 4:

All the figures in dollars.

• Initial balance: 76,026.60
• Initial balance + interest: 76,026.60(1 + 0.00175)¹² = 77,638.62
• Deposit at the end of the year: 28,000
• Final balance: 28,000 + 77,638.62 = 105,638.62

Assuming differences in rounding intermediate values, the answer is the option C.