Question

• (a): your answer is incorrect.• (b): your answer is incorrect.the lewises are saving up to go on a family vacation in 3 years. they invest $2600 into an account with an annual interest rate of 1.35% compounded annually.answer the questions below. do not round any intermediate computations, and round your final answers to the nearest cent. if necessary, refer to the list of financial formulas.(a) assuming no withdrawals are made, how much money is in the lewises account after 3 years?$(b) how much interest is earned on the lewises investment after 3 years?$

Explanation:

Step1: Identify compound interest formula

The formula for compound interest (annual compounding) is:
$$A = P(1 + r)^t$$
where $P=\$2600$ (principal), $r=0.0135$ (annual rate), $t=3$ (years).

Step2: Calculate account value after 3 years

Substitute values into the formula:
$$A = 2600(1 + 0.0135)^3 = 2600(1.0135)^3$$
First compute $(1.0135)^3 \approx 1.041109$
Then $A \approx 2600 \times 1.041109 = 2706.8834$

Step3: Calculate earned interest

Interest = Final amount - Principal
$$I = A - P = 2706.8834 - 2600 = 106.8834$$

Answer:

(a) $\$2706.88$
(b) $\$106.88$