Compound Interest and Percent Change

Write down the multiplier corresponding to each of these percentage changes:

1. a) An increase of $25\ \%$.

1. b) A decrease of $15\ \%$.

1. c) An increase of $3\ \%$.

1. d) A decrease of $60\ \%$.

1. e) An increase of $130\ \%$.

What percentage increase or decrease corresponds to each of these multipliers?

1. a) $1.45$

1. b) $0.82$

1. c) $2.1$

1. d) $0.05$

1. e) $1.06$

Apply the corresponding multiplier to calculate the final value:

1. a) A festival ticket costing $1{,}600$ pesos goes up by $15\ \%$.

1. b) A pair of sneakers costing $1{,}280$ pesos is discounted by $25\ \%$.

1. c) The monthly rent of $19{,}000$ pesos for a commercial space goes up by $4\ \%$.

After a discount of $25\ \%$ is applied, a coat costs $\$1\,080$.

1. a) What is the multiplier for the discount?

1. b) Calculate the initial price by dividing by the multiplier.

1. c) Check the result by applying the discount to the initial price you obtained.

A shop increases the price of its products by $20\ \%$ and, one month later, discounts them by $20\ \%$.

1. a) A pair of headphones initially cost $\$1\,000$. How much do they cost after the price increase? And after the discount?

1. b) Calculate the overall multiplier by multiplying the individual multipliers.

1. c) Have the prices returned to their initial value? What was the overall percentage change?

The shares of a technology company rose by $40\ \%$ in the first year, fell by $30\ \%$ in the second and rose by $10\ \%$ in the third.

1. a) Calculate the multiplier for each year and the overall multiplier for the three years.

1. b) If a share portfolio was worth $\$50\,000$ at the beginning, how much is it worth at the end of the third year?

1. c) What was the overall percentage change? Why does it not match the sum of the three percentages?

A saver deposits $\$40\,000$ in a deposit account at $4\ \%$ per annum compound interest; that is, each year the interest is added to the principal and also generates interest.

1. a) What does the principal become at the end of the first year?

1. b) What about at the end of the second year?

1. c) Why is the increase in the second year greater than that in the first year, if the percentage is the same?

Grandparents deposit $60{,}000$ pesos in a savings account at $5\ \%$ per annum compound interest for their granddaughter.

1. a) Write the expression that gives the final amount after $4$ years using a power.

1. b) Calculate the final amount using a calculator.

1. c) How many pesos correspond to interest?

Compare two ways of investing $20{,}000$ pesos for $3$ years at $6\ \%$ per annum, as shown in the figure:

• Simple interest: each year the same interest is generated on the initial principal.

• Compound interest: each year the interest is added to the principal.

1. a) Calculate the final amount with simple interest.

1. b) Calculate the final amount with compound interest.

1. c) What is the difference? Where does this difference come from?