square Ewan needs 10000 in 5 years for a trip. How much does he need to invest now if the bank offers 4.2% interest compounded quarterly?

## Step 1: Formula Identification<br />### We need to find the present value (P) given the future value (A), interest rate (r), number of times interest is compounded per year (n), and the number of years (t). The formula for compound interest is $A = P(1 + \frac{r}{n})^{nt}$. We need to solve for P.<br /><br />## Step 2: Variable Identification<br />### A = $10000 (future value), r = 0.042 (interest rate as a decimal), n = 4 (compounded quarterly), t = 5 (number of years).<br /><br />## Step 3: Solve for P<br />### Rearrange the formula to solve for P: $P = \frac{A}{(1 + \frac{r}{n})^{nt}}$. Substitute the values: $P = \frac{10000}{(1 + \frac{0.042}{4})^{4 \cdot 5}}$.<br /><br />## Step 4: Calculation<br />### Calculate the value inside the parenthesis: $1 + \frac{0.042}{4} = 1.0105$. Calculate the exponent: $4 \cdot 5 = 20$. Calculate the denominator: $(1.0105)^{20} \approx 1.2338$. Calculate P: $P = \frac{10000}{1.2338} \approx 8104.65$.