2 Piper and Ophelia deposit money into two different savings accounts. Piper deposits 1,840 into an account that earns 7% simple interest annually. Ophelia deposits 1,600 into an account that earns 7(1)/(4)% interest compounded annually. No additional deposits or withdrawals are made in either account. How much more money will Piper's account have than Ophelia's account at the end of 5 years? square I

To solve this problem, we need to calculate the amount of money in each account after 5 years and then find the difference between them.<br /><br />Given information:<br />- Piper deposits $1,840 into an account that earns 7% simple interest annually.<br />- Ophelia deposits $1,600 into an account that earns 7.25% interest compounded annually.<br />- The time period is 5 years.<br /><br />Step 1: Calculate the amount in Piper's account after 5 years.<br />Simple interest formula: A = P(1 + rt)<br />Where:<br />A = Amount in the account<br />P = Principal (initial deposit)<br />r = Interest rate (in decimal form)<br />t = Time (in years)<br /><br />Piper's account:<br />P = $1,840<br />r = 0.07 (7% simple interest)<br />t = 5 years<br /><br />A = 1,840(1 + 0.07 × 5)<br />A = 1,840(1 + 0.35)<br />A = 1,840(1.35)<br />A = $2,484<br /><br />Step 2: Calculate the amount in Ophelia's account after 5 years.<br />Compound interest formula: A = P(1 + r/n)^(nt)<br />Where:<br />A = Amount in the account<br />P = Principal (initial deposit)<br />r = Interest rate (in decimal form)<br />n = Number of times interest is compounded per year<br />t = Time (in years)<br /><br />Ophelia's account:<br />P = $1,600<br />r = 0.0725 (7.25% interest compounded annually)<br />n = 1 (compounded annually)<br />t = 5 years<br /><br />A = 1,600(1 + 0.0725/1)^(1 × 5)<br />A = 1,600(1 + 0.0725)^5<br />A = 1,600(1.0725)^5<br />A = 1,600 × 1.4116<br />A = $2,258.56<br /><br />Step 3: Calculate the difference between the amounts in Piper's and Ophelia's accounts.<br />Difference = Piper's account amount - Ophelia's account amount<br />Difference = $2,484 - $2,258.56<br />Difference = $225.44<br /><br />Therefore, Piper's account will have $225.44 more than Ophelia's account at the end of 5 years.