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### 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 . We need to solve for P.## Step 2: Variable Identification### A = P = \frac{A}{(1 + \frac{r}{n})^{nt}} P = \frac{10000}{(1 + \frac{0.042}{4})^{4 \cdot 5}} 1 + \frac{0.042}{4} = 1.0105 4 \cdot 5 = 20 (1.0105)^{20} \approx 1.2338 P = \frac{10000}{1.2338} \approx 8104.65$.