Problem
3. Rhonda deposits $\$ 5,600$ in a savings account that pays $1 \frac{1}{2} \%$ interest, compounded semi-annually. Round each of your answers to the nearest cent. a. How much interest does the account earn in the first 6 months? \[ \begin{aligned} I & =(5600)(0.0150)\left(\frac{6}{12}\right) \\ & =42 \end{aligned} \] b. What is the ending balance after 6 months? c. How much interest does the account earn in the second 6 months? d. What is the balance after 1 year? e. How much interest does the account earn in the first year? 4. Stephanie signed up for a direct deposit transfer into her savings account from her checking account. Every month, $\$ 125$ is withdrawn from her checking account. The interest in this account is $1.55 \%$, compounded monthly. How much money will be in the account at the end of 5.5 years? Round your answer to the nearest cent.
Solution
Step 1 ：\(I = (5600)(0.0150)\left(\frac{6}{12}\right)\)
Step 2 ：\(I = 42\)
Step 3 ：\(\text{Ending balance after 6 months} = 5600 + 42 = 5642\)
Step 4 ：\(I = (5642)(0.0150)\left(\frac{6}{12}\right)\)
Step 5 ：\(I = 42.315\)
Step 6 ：\(\text{Balance after 1 year} = 5642 + 42.315 = 5684.315\)
Step 7 ：\(\text{Interest earned in the first year} = 42 + 42.315 = 84.315\)
Step 8 ：\(\text{Future value of Stephanie's account} = 172228.19099601722\)
Step 9 ：\(\boxed{\text{a. }42.00}\)
Step 10 ：\(\boxed{\text{b. }5,642.00}\)
Step 11 ：\(\boxed{\text{c. }42.32}\)
Step 12 ：\(\boxed{\text{d. }5,684.32}\)
Step 13 ：\(\boxed{\text{e. }84.32}\)
Step 14 ：\(\boxed{\text{4. }172,228.19}\)
