Estimations Calculation - CCAT Test Prep

This type of question tests your understanding of calculating sequential percentage increases without resorting to complex multiplication. This skill can be useful for understanding real-life investment growth, property value appreciation, or price adjustments over time. The approach here focuses on breaking down the calculation into simple steps, avoiding fractions.
How to Calculate Consecutive Percentage Increases Step-by-Step Question 1 - Finding the Price After Two Consecutive Percentage Increases An investor purchases shares in a company for $10/share. The shares appreciate 20% in the first year and 25% the next. What is the price of the stock after two years?
A) $14.50/share
B) $15.00/share
C) $15.50/share
D) $16.50/share
E) $17.00/share
Step 1: Calculate the First Year's AppreciationThe initial price of the share is $10. To determine the price after a 20% increase:
First, 10% of $10 is:
10 ÷ 10 = 1
Since 20% is two times 10%:
1 × 2 = 2
Add the increase to the original price:
Price after first year 
    = 10 + 2 
    = 12
Step 2: Calculate the Second Year's AppreciationThe new price after the first year is $12. Now, let’s calculate the 25% increase:
10% of $12 is:
12 ÷ 10 = 1.2
25% can be thought of as two times 10% plus 5%:
Two times 10%:
1.2 × 2 = 2.4
5% is half of 10%:
1.2 ÷ 2 = 0.6

Add these together to find 25%:
2.4 + 0.6 = 3
Add the increase to the price after the first year:
Price after second year 
    = 12 + 3 
    = 15
Answer: $15.00/share
This approach keeps the calculations straightforward by breaking down percentages into smaller parts and adding them step by step.
Question 2 - Growth Over Consecutive Years An investor buys stock for $8/share. The stock appreciates by 15% in the first year and by 10% in the second year. What is the price of the stock after two years?
A) $9.24/share
B) $9.35/share
C) $9.68/share
D) $9.80/share
E) $10.00/share
Step 1: Calculate the First Year’s Appreciation10% of $8 is:
8 ÷ 10 = 0.8
5% is half of 10%:
0.8 ÷ 2 = 0.4
15% is 10% plus 5%:
0.8 + 0.4 = 1.2
Add the increase to the original price:
Price after first year 
    = 8 + 1.2 
    = 9.2
Step 2: Calculate the Second Year’s Appreciation10% of $9.20:
9.2 ÷ 10 = 0.92
Add this increase to the price after the first year:
Price after second year 
    = 9.2 + 0.92 
    = 10.12
Answer: $10.12/share
Question 3 - Compound Growth A piece of land is purchased for $15,000. Its value increases by 10% in the first year and then by 20% in the second year. What is the value of the land after two years?
A) $18,000
B) $18,150
C) $18,500
D) $19,800
E) $20,250
Step 1: Calculate the First Year’s Increase10% of $15,000:
15000 ÷ 10 = 1500
Add the increase to the original value:
Value after first year 
    = 15000 + 1500 
    = 16500
Step 2: Calculate the Second Year’s Increase20% can be broken down into two times 10%:
10% of $16,500:
16500 ÷ 10 = 1650
Two times 10%:
1650 × 2 = 3300

Add the increase to the value after the first year:
Value after second year 
    = 16500 + 3300 
    = 19800
Answer: $19,800
How to Solve These Questions Easily Break Down Percentages into Parts: Divide percentages into 10%, 5%, or 20% to simplify calculations.
Work Year by Year: Calculate each year separately, adding the growth step by step.
Avoid Fractions: Use simple multiplication and addition without fractions for more manageable calculations.
This approach will help you tackle these types of questions easily, without needing a calculator.
10 Practice Questions - Consecutive Percentage Increases An investor buys shares at $20 each. They increase by 10% in the first year and 15% in the second. What is the price after two years?
A) $23.00
B) $24.00
C) $24.10
D) $24.30
E) $25.00
A property worth $100,000 appreciates by 5% in the first year and 10% in the second. What is its value after two years?
A) $110,500
B) $112,500
C) $115,000
D) $117,000
E) $120,000
An item worth $50 appreciates by 20% the first year and by 10% the second year. What is the final price?
A) $60
B) $62
C) $63
D) $66
E) $68
A stock starts at $30/share. It appreciates by 15% in the first year and 25% in the second. What is the new price after two years?
A) $36
B) $37
C) $38
D) $39
E) $40
An apartment is bought for $150,000. Its value rises by 12% in the first year and by 18% in the second. What is its value after two years?
A) $178,200
B) $185,000
C) $189,720
D) $195,000
E) $200,000
A car bought for $25,000 increases in value by 8% in the first year and 12% in the second year. What is its value after two years?
A) $28,800
B) $29,120
C) $29,400
D) $30,000
E) $30,400
A bond worth $1,000 appreciates by 5% in the first year and by 8% in the second year. What is its final value?
A) $1,123
B) $1,134
C) $1,144
D) $1,150
E) $1,160
A machine costs $5,000. Its value grows by 10% in the first year and 15% in the second year. What is its new value?
A) $5,750
B) $5,875
C) $6,000
D) $6,250
E) $6,500
An investment of $4,000 grows by 7% in the first year and 5% in the second year. What is the value of the investment after two years?
A) $4,212
B) $4,224
C) $4,320
D) $4,400
E) $4,500
A savings account starts with $2,500. It earns 3% interest in the first year and 5% in the second year. What is the balance after two years?
A) $2,662
B) $2,675
C) $2,700
D) $2,725
E) $2,750
Answers C) $24.10
B) $112,500
C) $63
E) $40
C) $189,720
B) $29,120
C) $1,144
B) $5,875
B) $4,224
B) $2,675
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