Annuities

[Maximum mark: 6]

In this question give all answers correct to two decimal places.

Elena invests in a retirement plan in which equal payments of €$1500$ are made at the beginning of each year. Interest is earned on each payment at a rate of $2.49$ % per year, compounded annually.

1. Find the value of the investment after $25$ years. [3]
   

2. Find the amount of interest Elena will earn on the investment over $25$ years.[3]
   

[Maximum mark: 6]

In this question give all answers correct to two decimal places.

George invests in a retirement plan in which equal payments of $\$2750$ are made at the end of each year. Interest is earned on each payment at a rate of $3$ % per year, compounded semi-annually.

1. Find the value of the investment after $20$ years. [3]
   

2. Find the amount of interest George will earn on the investment over $20$ years.[3]
   

[Maximum mark: 6]

At the beginning of each year, Jack invests $\$5000$ in a savings account that pays $4\hspace{0.05em}\%$ annual interest, compounded quarterly

1. Find the number of years it will take until Jack has $\$100\hspace{0.15em}000$ in his account. [3]
   

At the beginning of each year, John invests $\$6000$ in a savings account that pays an annual interest rate, compounded semi-annually. After $20$ years John has $\$200\hspace{0.15em}000$ in his account.

2. Find the annual interest rate. [3]
   

[Maximum mark: 6]

Charles plans to invest in a retirement plan for $30$ years. In this plan, he will deposit $1000$ British pounds (GBP) at the end of every month and receive a $6.5\hspace{0.05em}\%$ interest rate per annum, compounded monthly.

1. Find the future value of the investment at the end of the $30$ years. Give your answer correct to the nearest pound.[3]
   

After the $30$-year period, Charles will start receiving regular monthly payments of $1500$ GBP.

2. Calculate the number of years it will take Charles's monthly retirement $\text{payments}$ to match the total amount originally invested. [3]