Question

Arianna invests $5800 in a new savings account which earns 5.0% annual interest, compounded quarterly. What will be the value of her investment after 4 years? Round to the nearest cent.

Answer 1

Given -

Amount Arianna invests = $5800

Annual interest = 5% compounded quarterly

To Find -

The value of her investment after 4 years =?

Step-by-Step Explanation -

We know the formula to calculate Investment Value =

`A\text{ = P\lparen1 + }(r)/(t)\text{\rparen}^(nt)`

Where,

A = Accumulated Value

P = Principal Amount = $5800

r = Rate of interest = 5% = 5/100 = 0.05

m = Number of times compoudeded = quarterly = 4

t = years = 4 Years

Now, putting all these values in the above formula, we get:

`\begin{gathered} A\text{ = 5800\lparen1 + }(.05)/(4)\text{\rparen}^(4*4) \\ \\ A\text{ = 5800\lparen1 + 0.0125\rparen}^(16) \\ \\ A\text{ = 5800\lparen1.0125\rparen}^(16) \\ \\ A\text{ = 5800}*1.2199 \\ \\ A\text{ = 7075.36} \end{gathered}`

Final Answer -

The value of her investment after 4 years = $7075 and 36 cents