Question

Hector puts $150 into an account when the interest rate is 4 percent. Later he checks his balance and finds he has about $175:48. How long did Hector wait to check his balance?

a) 4 years
b)4.5 years
c) 3 years
d) 3.5 years

Answer 1

Hector waited 3 years to check his balance.

Step-by-step explanation:

To solve this problem, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

• A is the final amount of money
• P is the principal amount (initial deposit)
• r is the annual interest rate (as a decimal)
• n is the number of times interest is compounded per year
• t is the number of years

In this case, Hector deposited $150, the interest rate is 4% (0.04 as a decimal), and the final amount is approximately $175.48. Let's calculate the number of years:

$175.48 = $150(1 + 0.04/n)^(n*t)

Simplifying this equation, we find:

(1 + 0.04/n)^(n*t) = 1.1699

By trying different values for n and t, we can find that when n = 4 and t = 3, the equation is satisfied:

(1 + 0.04/4)^(4*3) = 1.1699

Therefore, Hector waited 3 years to check his balance.