Question

royce deposits $1200 into a savings account that has an annual simple interest rate of 1.1%. after one year, he deposits another $1200 into the account. how much interest will royce have earned at the end of the first year? $ how much total interest will royce have earned at the end of the second year? $ what is the total amount in royce’s account at the end of the second year? $

Explanation:

Step1: Calculate Year 1 simple interest

Use formula $I = P \times r \times t$, where $P=\$1200$, $r=0.011$, $t=1$.
$I_1 = 1200 \times 0.011 \times 1 = 13.20$

Step2: Calculate Year 2 principal

Add initial and new deposit: $P_2 = 1200 + 1200 = 2400$

Step3: Calculate Year 2 simple interest

Use same rate and time:
$I_2 = 2400 \times 0.011 \times 1 = 26.40$

Step4: Calculate total 2-year interest

Sum Year 1 and Year 2 interest:
$I_{total} = 13.20 + 26.40 = 39.60$

Step5: Calculate total account value

Add total principal and total interest:
$A = (1200+1200) + 39.60 = 2439.60$

Answer:

1. Interest after first year: $\$13.20$
2. Total interest after second year: $\$39.60$
3. Total amount after second year: $\$2439.60$