Question

Albert and Samuel are given $10,000 each by their grandparents. Albert puts his money into the stock market immediately, earning 5% interest each year. Samuel holds onto his money for 2 years, before also investing in the stock market at the same interest rate as Albert. After 4 years, how much more money does Albert have?

A. $1025
B. $1130
C. $2050
D. $2155
E. $2260

Answer 1

Using the compound interest formula, after 4 years Albert has $12,155 and Samuel has $11,025. Therefore, Albert has $1,130 more than Samuel.

Step-by-step explanation:

The student is asking a compound interest problem where two individuals, Albert and Samuel, invest $10,000 each at a 5% annual interest rate. Albert invests immediately, while Samuel waits for 2 years before investing. After four years, we want to calculate how much more money Albert has compared to Samuel.

Albert's Investment

Albert invests for 4 years:

Future Value = $10,000 × (1 + 0.05)4

Future Value = $12,155

Samuel's Investment

Samuel invests for 2 years (since he waited for 2 years before investing):

• Future Value = $10,000 × (1 + 0.05)2
• Future Value = $11,025

Difference in value after 4 years = Albert's Future Value - Samuel's Future Value

Difference = $12,155 - $11,025 = $1,130

Therefore, Albert has $1,130 more than Samuel after 4 years.