**a. Fixed-term deposit for 3 months**
In this case, Chris will have 4 quarterly investments, each for 3 months.
**Investment 1:**
Interest earned after 3 months = (6.5/100)*$50000 = $3250
**Investment 2:**
Chris will reinvest the $3250 in addition to the original $50000, so the total investment amount will be $53250.
Interest earned after 3 months = (6.5/100)*$53250 = $3453.75
**Investment 3:**
Chris will reinvest the $3453.75 in addition to the original $50000, so the total investment amount will be $53453.75.
Interest earned after 3 months = (6.5/100)*$53453.75 = $3488.06
**Investment 4:**
Chris will reinvest the $3488.06 in addition to the original $50000, so the total investment amount will be $53488.06.
Interest earned after 3 months = (6.5/100)*$53488.06 = $3490.24
**Total interest earned after 12 months:**
$3250 + $3453.75 + $3488.06 + $3490.24 = **$13682.05**
**Graph:**
[Plot of the interest earned after 12 months for a fixed-term deposit for 3 months with reinvestment]
**b. Fixed-term deposit for 6 months**
In this case, Chris will have 2 semi-annual investments, each for 6 months.
**Investment 1:**
Interest earned after 6 months = (7/100)*$50000 = $3500
**Investment 2:**
Chris will reinvest the $3500 in addition to the original $50000, so the total investment amount will be $53500.
Interest earned after 6 months = (7/100)*$53500 = $3745
**Total interest earned after 12 months:**
$3500 + $3745 = **$7245**
**Graph:**
[Plot of the interest earned after 12 months for a fixed-term deposit for 6 months with reinvestment]
**c. Fixed-term deposit for 12 months**
In this case, Chris will have 1 annual investment, for 12 months.
Interest earned after 12 months = (7.5/100)*$50000 = **$3750**
**Graph:**
[Plot of the interest earned after 12 months for a fixed-term deposit for 12 months without reinvestment]
It is clear that the total interest earned after 12 months is highest for the fixed-term deposit for 3 months with reinvestment. This is because the interest is compounded every quarter, which means that the interest is earned on the interest that has already been earned.