Question

I dont quite understand this question, it talks about compound interest

Answer 1

Each person contribution = $2768.38

Step-by-step explanation:

Amount to be invested = P

Amount for vacation = $15000

This is the amount to be generated in the future from the investment

Future value = FV = $15000

time for investment = t = 10 years

rate = 6% per annum

r = 0.06

n = number of times compounded = semi-annually

n = 2

To determine the amount invested, we will apply compound interest formula:

`FV\text{ = P(1 +}(r)/(n))^(nt)`

substitute the values in the formula:

`\begin{gathered} 15000\text{ = P(1 + }(0.06)/(2))^(2*10) \\ 15000\text{ = P(1 + 0.03})^(20) \\ 15000\text{ = P(1.03})^(20) \\ \\ \text{divide both sides by (1.03})^(20)\colon \\ \frac{15000\text{ }}{\text{ (1.03})^(20)}\text{= }\frac{\text{P(1.03})^(20)}{\text{ (1.03})^(20)} \end{gathered}`
`\begin{gathered} \frac{15000\text{ }}{\text{ (1.03})^(20)}\text{ = P} \\ P\text{ = }8305.1363 \\ \\ To\text{ the nearest cent, amount invested = \$}8305.14 \end{gathered}`

Betty is splitting the cost of the vacation with her sister and brother.

The ratio in which the split was done is not stated.

To determine the amount each person will be paying, we will be assuming the split was done equally.

There are 3 people in total contributing to the purchase: Bettey, her sister and brother

Each person contribution = Amount invested/3

Each person contribution = 8305.14/3

Each person contribution = $2768.38