Accumulation with Regular Payments

$\displaystyle \pounds 400$ is deposited at the start of each year for $\displaystyle 3$ years into an account with an effective rate of interest of $\displaystyle 2\%$ per year.
Calculate the value of the account at the end of the $\displaystyle 3$ years.
Give your answer to the nearest penny.

$\displaystyle \pounds 250$ is deposited at the start of each year for $\displaystyle 2$ years into an account with an effective rate of interest of $\displaystyle 1.5\%$ per year.
Calculate the value of the account at the end of the $\displaystyle 2$ years.
Give your answer to the nearest penny.

$\displaystyle \pounds 1000$ is deposited at the start of each year for $\displaystyle 4$ years into an account with an effective rate of interest of $\displaystyle 3\%$ per year.
Calculate the value of the account at the end of the $\displaystyle 4$ years.
Give your answer to the nearest penny.

$\displaystyle \pounds 600$ is deposited at the start of each year for $\displaystyle 3$ years into an account with an effective rate of interest of $\displaystyle 4\%$ per year.
Calculate the value of the account at the end of the $\displaystyle 3$ years.
Give your answer to the nearest penny.

Zac deposits £500 into a bank account on 1 January 2018, 1 January 2019, and 1 January 2020.

The bank pays interest into his account at the end of every year, using the following annual effective rates:

• 2018: 3.3%
• 2019: 2.4%
• 2020: 1.0%

He makes no withdrawals from his account.

(a) Calculate the balance in Zac's account at the end of 2020.

On 1 January 2021 Zac deposits another £500 into his account. He makes no further deposits into his account in 2021.

(b) Calculate the annual effective rate of interest needed in 2021 for the account balance to be £2100 by the end of the year.