Mr Smith opened a bank account for his granddaughter Avril on the day she was born, January 5, 2006. He deposited \$4000 into the account.
Mrs Smith, Avril’s grandmother, deposited \$400 into this account on that day, and continues to do so by depositing \$400 every 3 months.
The balance at the end of each quarter for this investment, where interest is compounded quarterly, is given by A_n = 1.03 A_{n - 1} + 400, A_0 = 4\,400.
State the quarterly interest rate.
Find the nominal annual interest rate.
Find the balance on the day after Avril's first birthday.
Find the balance on the day after Avril's 12th birthday.
Bill opens an account to help save for a house. He opens the account at the beginning of 2013 with an initial deposit of \$40\,000 that is compounded annually at a rate of 3.7\% per annum. He makes further deposits of \$1000 at the end of each year.
How much money is in the account at the end of the first year?
Write a recursive rule for V_n in terms of V_{n - 1} and an initial condition V_0, that gives the value of the account after n years.
Calculate the total value of his savings at the beginning of 2021.
Hence determine how much interest Bill earned.
Sandy opens a savings account to motivate herself to save regularly. She opens the account at the start of September, 2013 with the intention of making regular deposits of \$110 at the end of each month. The interest rate for this account is 24\% per annum which compounds at the end of each month.
Find the monthly interest rate of this account.
If Sandy first invests \$2000 when she opens the account and makes no further deposits in September 2013, find the balance at the end of the first month.
Find the value of her savings account at the end of her second month.
Write a recursive rule for V_n in terms of V_{n - 1} that gives the value of the account after n months and an initial investment V_0.
Determine total value of her savings account at the start of September, 2019.
At the end of each month, Uther deposits \$2000 into a savings account to help him set money aside for bills. This savings account earns 24\% p.a. interest, compounded monthly.
The table below shows the first few months of 2015. All values in the table are in dollars:
| Monthly payment | Balance at the beginning of the month | Interest | Balance at end of the month | |
|---|---|---|---|---|
| March | 2000 | 20\,000 | 400 | 22\,000 |
| April | 2000 | 22\,400 | 448.00 | 24\,848.00 |
| May | 2000 | 24\,848.00 | 496.96 | 27\,344.96 |
| June |
Complete the row for June.
Write a recursive rule for V_n in terms of V_{n - 1} and an initial condition V_0, that gives the value of the account after n months.
Use the sequences facility on your calculator to determine the balance at the beginning of August 2016, assuming no withdrawals have been made.
Sarah initially deposits \$8000 into an investment account. At the end of each quarter Sarah makes an extra deposit of \$500.
The table below shows the first few quarters of 2011. All values in the table are in dollars:
| Balance at the beginning of quarter | Interest | Deposit | Balance at end of quarter | |
|---|---|---|---|---|
| Jan-Mar | 8000 | 320 | 500 | 8820 |
| Apr-Jun | 8820 | 352.80 | 500 | 9672.80 |
| Jul-Sep | 9672.80 | 386.91 | 500 | 10\,559.71 |
| Oct-Dec |
Calculate the quarterly interest rate.
Calculate the nominal annual interest rate.
Complete the row for the last quarter.
Write a recursive rule for V_n in terms of V_{n - 1} and an initial condition V_0, that gives the value of the account after n quarters.
Calculate the total value of her savings at the beginning of 2013.
The table below shows the first few years of an investment with regular deposits:
| Beginning balance | Interest | Deposit | End Balance | |
|---|---|---|---|---|
| 1 | y | 150 | 700 | 5\,850 |
| 2 | 5\,850 | 175.50 | 700 | 6\,725.50 |
| 3 | 6\,725.50 | x | 700 | 7\,627.27 |
| 4 | 7\,627.27 | 228.82 | 700 | w |
Find the value of:
Write a recursive rule for V_n in terms of V_{n - 1} and an initial condition V_0, that gives the value of the account after n years.
The total amount of this investment is withdrawn after 20 years. Find the value of the investment when its is withdrawn.
Calculate the total interest earned over the 20 years.
The table below shows the first few months of an investment with regular deposits. All values are given in dollars:
| Beginning balance | Interest | Deposit | End Balance | |
|---|---|---|---|---|
| Jan 2013 | y | 50 | 100 | 20\,150 |
| Feb 2013 | 20\,150 | 50.38 | 100 | 20\,300.38 |
| Mar 2013 | 20\,300.38 | x | 100 | 20\,451.13 |
| Apr 2013 | 20\,451.13 | 51.13 | 100 | 20\,602.26 |
Calculate the monthly interest rate.
Find the value of:
Write a recursive rule for V_n in terms of V_{n - 1}and an initial condition V_0, that gives the value of the account after n months.
The total amount of this investment is withdrawn after 6 years. Find the value of the investment when it is withdrawn.
Calculate the total interest earned over the 6 years.
A deposit of \$3000 is made on June 1, 2006 into an investment account and a deposit of \$400 is made each year on May 31.
The balance at the end of each 12-month period for this investment, where interest is compounded annually, is given by A_{n + 1} = 1.04 A_n + 400, and A_0 = 3000.
State the annual interest rate.
Find the balance on June 1, 2007.
Find the value of the investment on June 1, 2014.
Mr Jones opened a bank account for his granddaughter Victoria on the day she was born, January 5, 2007. He deposited \$3000. Mrs Jones, Victoria’s grandmother, also deposited \$500 into this account on that day, and continues to do so by depositing \$500 every 3 months.
The balance at the end of each quarter for this investment, where interest is compounded quarterly, is given by A_{n + 1} = 1.03 A_n + 500, A_0 = 3\,500.
State the quarterly interest rate.
Find the nominal annual interest rate.
Calculate the balance on the day after Victoria's first birthday.
Calculate the balance on the day after Victoria's 12th birthday.
Jenny is saving for a European holiday which will cost \$15\,000. She puts the \$5000 she has already saved in a savings account which offers interest compounded quarterly. She also makes a quarterly contribution of \$350. The progression of the investment is shown in the table below:
| Quarter | Account balance at start of quarter ($) | Interest ($) | Payment ($) | Account balance at end of quarter ($) |
|---|---|---|---|---|
| 1 | 5000 | 46.88 | 350 | 5396.88 |
| 2 | 5396.88 | 50.60 | 350 | 5797.48 |
| 3 | 5797.48 | A | 350 | B |
Find the interest rate per quarter for this account.
Calculate the value of: in dollars.
Write a recursive rule, T_{n + 1}, in terms of T_n that gives the balance in the account at the beginning of the \left(n + 1\right) th quarter.
Using the sequence facility of your calculator, how many whole quarters will it take to until she has enough money to go on the holiday?
If Jenny changes the payment to \$400 per quarter, how much sooner will she be able to go on holidays?
Dave opened a savings account at the beginning of February 2012, where the interest is compounded monthly. His account balance at the beginning of March, April and May are shown in the table:
Find the monthly interest rate.
Calculate the nominal annual interest rate.
How much did Dave deposit into this savings account when he opened it?
| Month | Balance |
|---|---|
| \text{March} | \$5100 |
| \text{April} | \$5202 |
| \text{May} | \$5306.04 |
Write a recursive rule for V_n in terms of V_{n - 1} and an initial condition for V_1, that gives the balance in the account at the beginning of the n th month.
Valerie is saving for a European holiday which will cost \$20\,000. She puts the \$8000 she has already saved in a savings account which offers 3.75\% p.a compounded quarterly. She also makes a quarterly contribution of \$400.
If N is the number of payments, use the financial application on your calculator to calculate the number of whole quarters it will take for Valerie to save the \$20\,000 required for the holiday.
An investor deposits \$12\,000 into a high earning account with interest of 2.5\% p.a. compounded monthly and makes \$80 per month deposits into the account.
If N is the number of payments, use the financial application of your calculator to calculate the number of whole months it will take until the investment doubles.
How much should the investor deposit each week if they want the original investment to triple at the end of three years?
Bill is saving for a skiing holiday which will cost \$3200. He puts the \$500 he has already saved into a savings account which offers 5.25\% p.a compounded monthly. He also makes a monthly contribution of \$100. Bill is interested in finding out how long it will take him to save up for his holiday.
If N is the number of payments, use the financial application of your calculator to calculate the number of whole months it will take for Bill to save the \$3200 required for the holiday.
A student deposits \$600 into a special students only savings account advertising an interest rate of 4.95\% p.a. compounded weekly. She also makes \$20 per week deposits into the account.
If N is the number of payments, use the financial application of your calculator to calculate the number of whole weeks it will take until the investment doubles. Assume there are 52 weeks in a year.
How much should the student deposit each week if they want the original investment to grow to \$2500 at the end of four years?
An investor deposits \$20\,000 into a high earning account with interest of 4.5\% p.a. compounded weekly and makes \$150 weekly deposits into the account.
If N is the number of payments, use the financial application of your calculator to Calculate the number of whole weeks it will take for the investment to double in value. Assume there are 52 weeks in a year.
How much should the investor deposit each week if they want the original investment to double at the end of three years?
Pauline and Yuri are saving for a house extension which will cost \$330\,000. They put the \$50\,000 they have already saved into an investment account which offers make a contribution of \$34 per day (which is approximately \$1000 per month).
If N is the number of payments, use the financial application of your calculator to calculate the number of whole years it will take for Pauline and Yuri to save the \$330\,000 required for the extension.
A self-funded retiree deposits \$200\,000 into a special savings fund advertising an interest rate of5.05\% p.a. compounded quarterly. An overseas pension also contributes \$360 per quarter into the account.
If N is the number of payments, use the financial application of your calculator to calculate the number of whole quarters it will take until the investment grows by \$15\,000.
A business man deposits \$23\,500 into an investment account advertising an interest rate of 3.85\% p.a. compounded daily. He also makes \$10 per day deposits into the account.
If N is the number of payments, use the financial application of your calculator to calculate the number of whole days it will take until the investment triples. Assume there are 365 days in a year.
How much should the business man deposit each day in dollars if they want the original investment to triple at the end of four years?
Kathleen aims to have \$250\,000 in her savings account by the time she is 33. She just turned 23 years old and has \$3\,325 in the account. The current interest rate is 3.2\% p.a. compounded monthly.
If N is the number of payments, use the financial application of your calculator to calculate the monthly payment required for Kathleen to save the \$25\,000 by the time she is 33 years old. Assume there are 365 days per year.
Amelia and Ryan are saving for a new caravan which will cost \$120\,000. They put the \$40\,000 they have already saved into an investment account which offers 3.015\% p.a. compounded weekly. They also make a contribution of \$50 per week.
If N is the number of payments, use the financial application of your calculator to calculate the number of whole weeks it will take for Amelia and Ryan to save the \$120\,000 required for the extension. Assume there are 52 weeks in a year.
The spreadsheet below shows the first year of an investment with regular deposits:
| A | B | C | D | E | |
|---|---|---|---|---|---|
| 1 | \text{Year} | \text{Beginning Balance} | \text{Interest} | \text{Deposit} | \text{End Balance} |
| 2 | 1 | 6\,000 | 660 | 500 | 7160 |
| 3 | |||||
| 4 | |||||
| 5 |
Calculate the annual interest rate for this investment.
Write a formula for cell \text{B3} in terms of one or more other cells.
Write a formula for cell \text{C6} in terms of \text{B6}.
Write a formula for cell E5 in terms of one or more other cells.
Using the spreadsheet facility on your calculator, reproduce this spreadsheet and determine the end balance for the 4th year.
Calculate the total interest earned over the 4 years.
The spreadsheet below shows the first month of an investment with regular deposits:
| A | B | C | D | E | |
|---|---|---|---|---|---|
| 1 | \text{Initial Investment} | 20\,000 | |||
| 2 | \text{Annual Interest Rate} | 0.072 | |||
| 3 | \text{Monthly Deposit} | 400 | |||
| 4 | |||||
| 5 | |||||
| 6 | \text{Month} | \text{Beginning Balance} | \text{Interest} | \text{Deposit} | \text{End Balance} |
| 7 | 1 | 20\,000 | 120 | 400 | 20\,520 |
| 8 | |||||
| 9 | |||||
| 10 |
Calculate the monthly interest rate for this investment.
Write a formula for cell \text{B7} in terms of one or more cells.
Write a formula for cell \text{C7} in terms of one or more cells.
Write a formula for cell \text{E7} in terms of one or more cells.
Using the spreadsheet facility on your calculator, reproduce this spreadsheet and determine the end balance for the 5th year.
Calculate the total interest earned over the 60 months.