Question

Use the formula S=P(1+r)t to complete parts (a) and (b).a. Graph the function that gives the future value of $60,000 invested at 5%, compounded annually, for t years, 0≤t≤12.b. Find the future value of $60,000 invested for 5 years at 5% compounded annually.

Answer 1

The Graph of a Function

The formula:

`S=P(1+r)^t`

Will be used to calculating the future value of two conditions a and b

a) P = $60,000, r = 5% = 0.05, 0 ≤ t ≤ 12.

Substitute some selected values of t in the given interval.

For t=0:

`\begin{gathered} S=60,000(1+0.05)^0 \\ S=60,000\cdot1.05^0 \\ S=60,000 \end{gathered}`

For t=3:

`\begin{gathered} S=60,000(1+0.05)^3 \\ S=60,000\cdot1.05^3 \\ S=69,457.50 \end{gathered}`

For t=6:

`\begin{gathered} \\ S=60,000\cdot1.05^6 \\ S=80,405.74 \end{gathered}`

For t=9:

`\begin{gathered} S=60,000\cdot1.05^9 \\ S=93,079.69 \end{gathered}`

For t=12:

`\begin{gathered} S=60,000\cdot1.05^(12) \\ S=107,751.38 \end{gathered}`

The graph that looks closer to the graph above is B.

b. Calculate the future value for t=5 years.

`\begin{gathered} S=60,000\cdot1.05^5 \\ S=76,576.89 \end{gathered}`