Alan received the proceeds from an inheritance on April 15. He wants to set aside enough on April 16 so that he will have $18,000 available on October 8 to purchase a car when the new models are introduced. If the current interest rate on 91- to 180-day deposits is 6.25%, what amount should he place in the term deposit? For full marks your answer(s) should be rounded to the nearest cent.

To determine the amount Alan should place in the term deposit, we need to calculate the present value of $18,000, which he wants to have on October 8. The interest rate given is 6.25% per annum, and we need to adjust it for the specific period between April 16 and October 8.

First, let's calculate the number of days between April 16 and October 8:

• April 16 to April 30: 15 days
• May: 31 days
• June: 30 days
• July: 31 days
• August: 31 days
• September: 30 days
• October 1 to October 8: 8 days

Total number of days = 15 + 31 + 30 + 31 + 31 + 30 + 8 = 176 days

Next, we need to convert the annual interest rate to a daily interest rate. The annual interest rate is 6.25%, so the daily interest rate is:

$\text{Daily interest rate} = \frac{6.25\%}{365} = \frac{0.0625}{365} \approx 0.0001712329$

Now, we need to find the present value (PV) of $18,000 using the formula for compound interest:

$PV = \frac{FV}{(1 + r)^n}$

where:

• $FV$ is the future value ($18,000)
• $r$ is the daily interest rate (0.0001712329)
• $n$ is the number of days (176)

Plugging in the values:

$PV = \frac{18,000}{(1 + 0.0001712329)^{176}}$

First, calculate $(1 + 0.0001712329)^{176}$:

$(1 + 0.0001712329)^{176} \approx 1.0305$

Now, calculate the present value:

$PV = \frac{18,000}{1.0305} \approx 17,465.92$

Therefore, Alan should place approximately $17,465.92 in the term deposit on April 16 to have$18,000 available on October 8.