Simple Interest 1

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Year 10

Consumer Maths

Simple Interest

Simple Interest 1

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Question 1 of 5

1. Question
Steve invested $$4{,}000$ in a savings account. The interest rate is $3.5 %$ $3.5%$ per year. Find the interest earned if the amount was kept in the bank for $3$ $3$ years.
- $Interest Earned = $$ $\text(Interest Earned )=$$ (420)
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Simple Interest Formula

$I =$ $I =$ $P$ $P$ $r$ $r$ $t$ $t$

Identify the given values

Principal Value $= P = $4{,}000$

Interest Rate $= r = 3.5 %$ $= r = 3.5%$ per annum

Time Elapsed $= t = 3$ $= t = 3$ years

First, express the rate as a decimal

$3.5 % = 0.035$ $3.5% = 0.035$

Solve for the Interest $(I),$ $(I),$ using the formula

$I$ $I$ $=$ $=$ $P$ $P$ $r$ $r$ $t$ $t$ Simple Interest Formula

$=$ $=$ $$4{,}000$ $\times$ $times$ $0.035$ $0.035$ $\times$ $times$ $3$ $3$ Plug in the known values

$=$ $=$ $$ 420$ $$420$

$$ 420$ $$420$ interest earned
Question 2 of 5

2. Question
Mary invested $$3{,}000$ in a savings account. The interest rate is $9.5 %$ $9.5%$ per year and is not compounded. Find the interest earned if the amount was kept in the bank for $10$ $10$ months.

Round your answer to two decimal places
- $Interest Earned = $$ $\text(Interest Earned )=$$ (237.50)
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Simple Interest Formula

$I =$ $I =$ $P$ $P$ $r$ $r$ $t$ $t$

Identify the given values

Principal Value $= P = $3{,}000$

Interest Rate $= r = 9.5 %$ $= r = 9.5%$ per annum

Time Elapsed $= t = 10$ $= t = 10$ months

First, express the rate as a decimal

$9.5 % = 0.095$ $9.5% = 0.095$

We are given a rate per annum, so we need to solve for the rate per month

Rate per month $=$ $=$ Rate $(r)$ $(r)$ per annum $\div 12$ $divide 12$

$=$ $=$ $0.095$ $0.095$ $\div 12$ $divide 12$

$=$ $=$ $0.00792$ $0.00792$ Interest rate per month

Solve for the Interest $(I),$ $(I),$ using the formula

$I$ $I$ $=$ $=$ $P$ $P$ $r$ $r$ $t$ $t$ Simple Interest Formula

$=$ $=$ $$3{,}000$ $\times$ $times$ $0.00792$ $0.00792$ $\times$ $times$ $10$ $10$ Plug in the known values

$=$ $=$ $$ 237.50$ $$237.50$

$$ 237.50$ $$237.50$ interest earned

Question 3 of 5

If you put money into a savings account that earns $$ 147.00$ $$147.00$ over seven years at a rate of $3 %$ $3%$ , how much money did you put into the account?

Principal $= $$ $=$ \$ (700)

Incorrect

Simple Interest Formula

I = P r t

$color(purple)(I)=color(forestgreen)(P)color(royalblue)(r)color(tomato)(t)$

Labelling the given values

Interest

= I = $ 147

$=I=$147$

Principal Value

= P = ?

$=P=?$

Rate

= r = 3 %

$=r=3%$ per annum

Time Elapsed

= t = 7

$=t=7$ years

First, express the rate as a decimal

3 % = 0.03

$3% = 0.03$

Solve for the Principal

(P),

$(P),$ using the formula

$I$ $color(purple)(I)$	$=$ $=$	$P r t$ $color(forestgreen)(P)color(royalblue)(r)color(tomato)(t)$	Simple Interest Formula
$$ 147$ $color(purple)($147)$	$=$ $=$	$P \times 0.03 \times 7$ $color(forestgreen)(P) color(black)(times) color(royalblue)(0.03) color(black)(times) color(tomato)(7)$	Plug in the known values
$$ 147$ $$147$	$=$ $=$	$P \times 0.21$ $Ptimes0.21$	Simplify
$$ 700$ $$700$	$=$ $=$	$P$ $P$	Divide both sides by $0.21$ $0.21$ .
$P$ $P$	$=$ $=$	$$ 700$ $$700$	Reverse the sides so that the unknown variable $P$ $P$ is on the left-hand side.

The Principal is

$ 700

$$700$ .

Question 4 of 5

How much interest is earned on a principal of $200 invested at an interest rate of 6% for eight years?

Interest Earned $= $$ $=$ \$ (96)

Incorrect

Simple Interest Formula

I = P r t

$color(purple)(I)=color(forestgreen)(P)color(royalblue)(r)color(tomato)(t)$

Labelling the given values

Interest

= I = ?

$=I=?$

Principal Value

= P = $ 200

$=P=$200$

Rate

= r = 6 %

$=r=6%$ per annum

Time Elapsed

= t = 8

$=t=8$ years

First, express the rate as a decimal

6 % = 0.06

$6% = 0.06$

Solve for the Interest

(I),

$(I),$ using the formula

$I$ $color(purple)(I)$	$=$ $=$	$P r t$ $color(forestgreen)(P)color(royalblue)(r)color(tomato)(t)$	Simple Interest Formula
	$=$ $=$	$$ 200 \times 0.06 \times 8$ $color(forestgreen)($200) color(black)(times) color(royalblue)(0.06) color(black)(times) color(tomato)(8)$	Plug in the known values
	$=$ $=$	$$ 96$ $$96$

$ 96

$$96$ interest earned

Question 5 of 5

5. Question
If an investment over eight years that gives $$ 160.00$ $$160.00$ in interest results in a final balance of $$ 610.00$ $$610.00$ , what was the original investment?
- Principal $= $$ $=$ \$ (450)
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Simple Interest Formula

$I = P r t$ $color(purple)(I)=color(forestgreen)(P)color(royalblue)(r)color(tomato)(t)$

Labelling the given values

Interest $= I = $ 160$ $=I=$160$

Principal Value $= P = ?$ $=P=?$

Rate $= r = ?$ $=r=?$ per annum

Time Elapsed $= t = 8$ $=t=8$ years

Solve for the Principal $(P),$ $(P),$ by subtracting the final total $$ 610$ $$610$ from the interest earned $$ 160$ $$160$ .

The Principal is $$ 450$ $$450$ .

The Principal is $$ 450$ $$450$ .

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Quiz summary

Information

1. Question

Hint

Keep Going!

Simple Interest Formula

Identify the given values

2. Question

Hint

Fantastic!

Simple Interest Formula

Identify the given values

3. Question

Keep Going!

Simple Interest Formula

Labelling the given values

4. Question

Keep Going!

Simple Interest Formula

Labelling the given values

5. Question

Keep Going!

Simple Interest Formula

Labelling the given values

Quizzes

$I$ $I$	$=$ $=$	$P$ $P$ $r$ $r$ $t$ $t$	Simple Interest Formula
	$=$ $=$	$$4{,}000$ $\times$ $times$ $0.035$ $0.035$ $\times$ $times$ $3$ $3$	Plug in the known values
	$=$ $=$	$$ 420$ $$420$

Rate per month	$=$ $=$	Rate $(r)$ $(r)$ per annum $\div 12$ $divide 12$
	$=$ $=$	$0.095$ $0.095$ $\div 12$ $divide 12$
	$=$ $=$	$0.00792$ $0.00792$	Interest rate per month