4. Suppose you have 10,000 to deposit into a savings account. The bank offers an interestrate of 2.75% compounded monthly. How much will be in your account after 4 years? A=P(1+(r)/(n))^nt

To solve this problem, we can use the formula for compound interest:

$$A = P(1 + \frac{r}{n})^{nt}$$

where:
- $$A$$ is the final amount in the account
- $$P$$ is the principal amount (initial deposit)
- $$r$$ is the annual interest rate (in decimal form)
- $$n$$ is the number of times the interest is compounded per year
- $$t$$ is the time in years

Given information:
- $$P = \$10,000$$
- $$r = 2.75\% = 0.0275$$
- $$n = 12$$ (compounded monthly)
- $$t = 4$$ years

Substituting the values into the formula:

$$A = 10,000 \times (1 + \frac{0.0275}{12})^{12 \times 4}$$
$$A = 10,000 \times (1 + 0.00229167)^{48}$$
$$A = 10,000 \times (1.00229167)^{48}$$
$$A = 10,000 \times 1.1166$$
$$A = \$11,166$$

Therefore, the amount in the account after 4 years will be $11,166.