Question

60 points! Please answer fast and show your work... Thank you!
You would like to purchase the car in 2 years. How much money will you need to invest at a 3.3% interest rate compounded annually in order to have $9500 in 2 years? Use the compound interest formula A = P (1 + i)n. (Round final answer to the nearest cent, but otherwise don’t round any intermediate values)

Answer 1

Answer:

$ 8902.72

Step-by-step explanation:

We would like to calculate the money which we need to invest at 3.3% rate compounded annually for two years . We know that ,

$\longrightarrow \boldsymbol{ A = P \bigg(1+\dfrac{R}{100}\bigg)^n }$

where the symbols have their usual meaning . So here ,

• Amount = $ 9500
• time = 2 years
• Rate = 3.3%
• P = The money we need to invest (?)

$\longrightarrow \ 9500 = P \bigg( 1+\dfrac{3.3}{100}\bigg)^2$

Simplify RHS ,

$\longrightarrow \ 9500 = P \bigg(\dfrac{100+3.3}{100}\bigg)^2$

Simplify Nr . in RHS ,

$\longrightarrow \ 9500 =P\bigg(\dfrac{103.3}{100}\bigg)^2$

Isolate P ,

$\longrightarrow P = \dfrac{ \ 9500\times 100\times 100}{103.3\times 103.3}$

Simplify ,

$\longrightarrow \underline{\underline{\boldsymbol{ P = \ 8902.72 }}}{}$

And we are done !

Answer 2

$\bold{Formula: A = P(1 + \frac{r}{100})^{(n)}}$

Where

• A = Amount
• P = Principal
• R = Rate
• N = time compounded

$\bold{Solution : } \\ \\ \: \: \: \: \tt \: A = 9,500(1+\frac{3.3\%}{100})^{(2)} \\ \: \: \: \: \: \: \tt \: A = 9,500(1+ 0.033)^{(2)} \\ \tt \: A = 9,500(1.033)^{(2)} \: \: \\ \tt \: A = 10,137.34 \qquad \: \: \:$

therefore,I need $10,137.34 if would like to purchase the car.