Combining Interest Rates

$\displaystyle \pounds 5000$ is invested. The effective rate of interest is $\displaystyle 3.6\%$ per year for the first $\displaystyle 2$ years, then $\displaystyle 2.1\%$ per year for the next $\displaystyle 3$ years.
Calculate the value of the investment after $\displaystyle 5$ years.
Give your answer to the nearest penny.

A loan of $\displaystyle \pounds 4200$ is charged an effective rate of interest of $\displaystyle 0.9\%$ per month for $\displaystyle 6$ months, then $\displaystyle 2.4\%$ per quarter for a further $\displaystyle 2$ quarters.
No repayments are made.
Calculate the amount owed at the end.
Give your answer to the nearest penny.

$\displaystyle \pounds 8000$ is invested at an effective rate of interest of $\displaystyle 1.4\%$ per half-year for $\displaystyle 2$ years, then $\displaystyle 3.2\%$ per year for $\displaystyle 1$ year.
Calculate the value of the investment after $\displaystyle 3$ years.
Give your answer to the nearest penny.

$\displaystyle \pounds 1500$ is invested at an effective rate of interest of $\displaystyle 2.5\%$ per year for $\displaystyle 3$ years, then $\displaystyle 0.3\%$ per month for $\displaystyle 4$ months.
Calculate the value of the investment after the full period.
Give your answer to the nearest penny.

The average price of petrol increased at the following annual effective rates:

• March 2018 to 2019: 2.1%
• March 2019 to 2020: 0.5%
• March 2020 to 2021: 2.0%

(a) Calculate the overall percentage increase in the average price of petrol over the three years from March 2018 to March 2021.

The average price of petrol in March 2021 was 136.4 pence per litre.

(b) Hence calculate the average cost of filling a 45-litre tank with petrol in March 2018.

Taylor opens a savings account on 1 April 2021 with an initial deposit of £400.

The effective rates of interest for the savings account are as follows.

Dates	Interest rate
1 April 2021 to 31 January 2022	1.2% per year
1 February 2022 to 31 July 2022	0.11% per month
From 1 August 2022	1.7% per year

Taylor makes further deposits of £200 on 1 August 2021 and £250 on 1 April 2022.

(a) Calculate the balance in Taylor's savings account on 31 July 2022.

Taylor made a final deposit into this account on 1 August 2022. On 1 December 2022, their savings account balance was £1000.

(b) Calculate how much they deposited on 1 August 2022.

Ewa deposited £4500 in a variable rate savings account on 1 January 2021. The effective rates of interest for the savings account are as follows:

Dates	Interest rate
1 January 2021 to 31 March 2021	0.415% per month
1 April 2021 to 31 December 2021	4.7% per year
From 1 January 2022	2.6% per year

(a) Calculate Ewa's balance on 1 January 2024.

On 1 January 2022 Blair opened an account with the same effective rates of interest. Blair has a savings goal of £6000 by 1 January 2024.

(b) Calculate the minimum deposit Blair should have made on 1 January 2022 to achieve this savings goal.