Percentage: reverse percent and simple interest

Advanced Math 7 · Unit 7 · percent-simple-interest · Teacher edition

percent-simple-interest

Name ______________________________Date ______________

1.
Find the simple interest earned on $500 at $4\%$ per year for $3$ years, in dollars.
Answer: ______________
2.
After a $20\%$ discount, a jacket costs $72. What was the original price, in dollars?
Answer: ______________
3.
Priya deposits $1,200 in an account paying $5\%$ simple interest per year. After how many years will the account hold $1,500?
Answer: ______________
4.
A video game is on sale for $60 after a $25\%$ discount. What was the original price?
1. (A)
  $45
2. (B)
  $75
3. (C)
  $80
4. (D)
  $85
5.
Account A starts with $800 and earns $6\%$ simple interest per year. Account B starts with $1,000 and earns $4\%$ simple interest per year. After how many years do the two accounts hold the same amount?
1. (A)
  $5$
2. (B)
  $10$
3. (C)
  $20$
4. (D)
  $25$
5. (E)
  $50$

Answer key — Percentage: reverse percent and simple interest

1.
60percent-simple-interest-01
$I = Prt = 500 \times 0.04 \times 3 = \mathbf{60}$ dollars. (The account then holds $500 + 60 = 560$ dollars.)
2.
90percent-simple-interest-02
$0.8P = 72 \Rightarrow P = 72 \div 0.8 = \mathbf{90}$ . Check: $20\%$ of $90$ is $18$ , and $90 - 18 = 72$ . ✓
3.
5percent-simple-interest-03
Interest needed $= 300$ . Per year: $1{,}200 \times 0.05 = 60$ . Years $= 300 \div 60 = \mathbf{5}$ . Or with $A = P(1 + rt)$ : $1{,}500 = 1{,}200(1 + 0.05t) \Rightarrow 1.25 = 1 + 0.05t \Rightarrow t = 5$ .
4.
(C)
$80
percent-simple-interest-04
One quarter of the original is $20$ , so the original is $4 \times 20 = \mathbf{80}$ dollars. Check: $25\%$ of $80$ is $20$ ; $80 - 20 = 60$ . ✓ ($75 adds $25\%$ of $60 — the wrong base. $45 discounts the sale price again.)
5.
(D)
$25$
percent-simple-interest-05
$800 + 48t = 1{,}000 + 40t \Rightarrow 8t = 200 \Rightarrow t = \mathbf{25}$ years. Check: A holds $800 + 1{,}200 = 2{,}000$ and B holds $1{,}000 + 1{,}000 = 2{,}000$ . ✓ ( $5$ divides the $200 gap by B's $40$ per year instead of by the $8$ per year difference.)