Question

Sam requires $5,000 at the end of 6 years. He can deposit money in an account that earns 5% interest annually. How much money should he deposit today to meet this goal?

a. $3,731
b. $2,474
c. $1,000
d. $2,500

Answer 1

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.