Question

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: Recall compound interest formula

The formula for compound amount (annual compounding) is $A = P(1 + r)^t$, where $P$ is principal, $r$ is annual rate, $t$ is time in years.

Step2: Plug in given values

$P = 2600$, $r = 0.0135$, $t = 3$
$A = 2600(1 + 0.0135)^3$

Step3: Calculate intermediate value

First compute $1.0135^3 \approx 1.041109$

Step4: Find total account value

$A = 2600 \times 1.041109 \approx 2706.88$

Step5: Calculate earned interest

Interest = Total amount - Principal
$I = 2706.88 - 2600 = 106.88$

Answer:

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