Two brothers, Marvin and Luis, each invest $5,000 into accounts that earn 5% interest. Neither brother deposits or withdrawals anything from the account for 25 years. If Marvin's account earns compound interest and Luis's account earns simple interest, who will earn more interest after 25 years, and by how much?
Marvin will earn $16,931.77 more in interest than Luis.
Marvin will earn $5,681.77 more in interest than Luis.
Marvin will earn $10,681.77 more in interest than Luis.
Luis will earn $11,250 more in interest than Marvin.
To calculate the amount of interest each brother earns after 25 years, we first need to find the future value of their investments.
For Marvin's account with compound interest:
Future Value = $5,000 * (1 + 0.05)^25
Future Value = $5,000 * (1.05)^25
Future Value = $5,000 * 3.960234
Future Value = $19,801.17
Interest Earned = Future Value - Initial Investment
Interest Earned = $19,801.17 - $5,000
Interest Earned = $14,801.17
For Luis's account with simple interest:
Simple Interest = Principal * Rate * Time
Simple Interest = $5,000 * 0.05 * 25
Simple Interest = $5,000 * 0.05 * 25
Simple Interest = $6,250
Therefore, after 25 years, Marvin will earn $14,801.17 in interest, while Luis will earn $6,250 in interest. The difference between the two amounts is:
$14,801.17 - $6,250 = $8,551.77
Therefore, Marvin will earn $8,551.77 more in interest than Luis.