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Compound Interest

Compound Interest

If you borrow money (sometimes called a loan), usually you have to repay the amount you borrowed plus .
One way of calculating how much interest to pay is called interest.
For example, if a bank charges compound interest at $10\%$ p.a. (per annum, which means "per "), the borrower must pay $10\%$ of the loan including the interest that has .

A bank charges $10\%$ p.a. compound interest.

If you borrow $\$600$ for $3$ years:
After the first year, the interest you owe is $\$$ .
Therefore, after $1$ year, the total amount you owe is $\$$ .

After the second year, the interest you owe is $10\%$ of the amount you owe at the end of the first year, which is $\$$ .
Therefore, after $2$ years, the total amount you owe is $\$$ .

After the third year, the interest you owe is $10\%$ of the amount you owe at the end of the second year, which is $\$$ .
Therefore, after $3$ years, the total amount you owe is $\$$ .
The total amount of interest paid is $\$$


If you borrow $\$1000$ for $5$ years:
After the first year, the interest you owe is $\$$ .
Therefore, after $1$ year, the total amount you owe is $\$$ .

After the second year, the interest you owe is $10\%$ of the amount you owe at the end of the first year, which is $\$$ .
Therefore, after $2$ years, the total amount you owe is $\$$ .

After the third year, the interest you owe is $10\%$ of the amount you owe at the end of the second year, which is $\$$ .
Therefore, after $3$ years, the total amount you owe is $\$$ .

After the fourth year, the interest you owe is $10\%$ of the amount you owe at the end of the third year, which is $\$$ .
Therefore, after $4$ years, the total amount you owe is $\$$ .

After the fifth year, the interest you owe is $10\%$ of the amount you owe at the end of the fourth year, which is $\$$ .
Therefore, after $5$ years, the total amount you owe is $\$$ .
The total amount of interest paid is $\$$ .


Is there a faster way to calculate this?
Amount borrowed After 1 year After 2 years After 3 years After 4 years After 5 years
$\$1000$ $\$1100$ $\$1210$ $\$1331$ $\$1464.10$ $\$1610.51$
The total amount owed increases by $10\%$ each year.

To increase by $10\%$, we multiply by .

The total amount owed after $1$ year $=\$1000\times$

The total amount owed after $2$ years $=\$1000\times$ $\times$ $=\$1000\times 1.1$

The total amount owed after $3$ years $=\$1000 \times 1.1 \times 1.1 \times 1.1 = \$1000 \times 1.1$

The total amount owed after $4$ years $=\$1000 \times 1.1$

The total amount owed after $5$ years $=\$1000 \times$

The total amount of interest paid is $\$1610.51-\$$ $=\$$

Sungjae borrowed $\yen 30,000$ from a loan company that charges $18\%$ p.a. compound interest.
Round your answers to the nearest yen. You don’t need to include the $\yen$ symbol.

a) Find the total amount Sungjae must pay back after 4 years.
b) Find the total interest Sungjae pays after 4 years.

a)

b)

Jess invests $£5000$ in investments that earn $9.7\%$ p.a. compound interest.
Round your answers to two decimal places. You don’t need to include the $£$ or $\%$ symbol.

a) Find the total value of Jess’s investment after 6 years.
b) Find the total interest earned in the 6 year period.
c) Find the total percentage increase of Jess’s investment after 6 years.

a)

b)

c)

Chloe wants to invest $\$4000$ for 5 years. She has two options – an investment with:
Option 1: an interest rate of $8\%$ p.a. simple interest
Option 2: an interest rate of $7\%$ p.a. compound interest

a) Find the value of the investment at the end of 5 years if she chooses Option 1.
You don’t need to include the $\$$ symbol.
b) Find the value of the investment at the end of 5 years if she chooses Option 2.
Round your answer to two decimal places. You don’t need to include the $\$$ symbol.
c) Which Option gives her more money after 5 years? Type “1” or “2”.

a)

b)

c)

A bank pays compounded interest at $1\%$ p.a. Sigmund wants to invest for 10 years so that the value becomes $\$10000$ at the end of the 10 years. How much money does Sigmund need to invest now?
Round your answer to two decimal places. You don’t need to include the $\$$ symbol.

Erin invested $\yen 10000$ for 1 year. The value after 1 year was $\yen 15000$.
What was the annual interest rate?
You don't need to include the $\%$ symbol.

Cam invested $\yen 10000$ for 2 years. The value after 2 years was $\yen 15000$.
What was the annual interest rate?
Round your answer to one decimal place. You don't need to include the $\%$ symbol.

Jordan invested $\yen 10000$ for 3 years. The value after 3 years was $\yen 15000$.
What was the annual interest rate?
Round your answer to one decimal place. You don't need to include the $\%$ symbol.

Zoe invested $\yen 10000$ for 4 years. The value after 4 years was $\yen 15000$.
What was the annual interest rate?
Round your answer to one decimal place. You don't need to include the $\%$ symbol.