Final answer:
To meet his goal of $5,000 at the end of 6 years with a 5% annual interest rate, Sam should deposit approximately $3,731.08 today.
Therefore, the correct answer is: option a). $3,731
Step-by-step explanation:
To find out how much money Sam should deposit today to meet his goal of $5,000 at the end of 6 years with a 5% annual interest rate, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
- A is the future amount
- P is the principal amount (the amount to be deposited)
- r is the annual interest rate (as a decimal)
- n is the number of times the interest is compounded per year (here, annually)
- t is the number of years
Plugging in the values, we get:
$5,000 = P(1 + 0.05/1)^(1*6)
Simplifying the equation, we find:
P = $5,000 / (1.05^6)
P ≈ $3,731.08
Therefore, Sam should deposit approximately $3,731.08 today to meet his goal.