Question

Cassandra Dawson wants to save for a trip to Australia. How much money does she need for her trip?

A) $8000
B) $10000
C) $12000
D) $15000

Answer 1

Cassandra Dawson needs to invest approximately $2,538 annually, rounded to the nearest dollar, with a 6.8% annual interest rate, for four years, to reach her $12,000 savings goal for a trip to Australia. (options B and C)

To calculate the annual investment needed to reach the target amount, we can use the future value of an annuity formula:

`\[ FV = P * \left( ((1 + r)^n - 1)/(r) \right) \]`

Where:

- FV is the future value (target amount) = $12,000

- P is the annual investment

- r is the annual interest rate = 6.8% or 0.068

- n is the number of years = 4

Let's rearrange the formula to solve for P:

`\[ P = (FV)/(\left( ((1 + r)^n - 1)/(r) \right)) \]`

Now, substitute the values:

`\[ P = (12,000)/(\left( ((1 + 0.068)^4 - 1)/(0.068) \right)) \]`

Calculate this expression to find the annual investment needed.

`\[ P \approx (12,000)/(\left( ((1.068)^4 - 1)/(0.068) \right)) \]\[ P \approx (12,000)/(\left( (1.310796 - 1)/(0.068) \right)) \]\[ P \approx (12,000)/(\left( (0.310796)/(0.068) \right)) \]\[ P \approx (12,000)/(4.573235) \]\[ P \approx 2,622.74 \]`

Therefore, the closest rounded answer is
`\( \text{B. } \$2,538 \)`.

The question states that Cassandra Dawson needs $12,000 for her trip to Australia. Therefore, the correct answer is C) $12,000.

The complete question is:

Cassandra Dawson wants to save for a trip to Australia. She will need $12,000 at the end of four years. She can invest a certain amount at the beginning of each of the next four years in a bank account that will pay her 6.8 percent annually. How much will she have to invest annually to reach her target? (Round to the nearest dollar.)

A. $3,000

B. $2,538

C. $2,711

D. $2,980

How much money does she need for her trip?

A) $8000

B) $10000

C) $12000

D) $15000