Question

You deposit $400 in an account that pays 2.4% annual interest compounded monthly a. When does your balance first exceed $500? after years and months b. Use the compound interest formula to find the balance after this amount of time. The balance is $​

Answer 1

To determine when the balance will exceed $500, we can use the compound interest formula: A = P(1 + r/n)^(nt). By solving for t, we find that the balance will first exceed $500 after approximately 2 years and 1 month.

Step-by-step explanation:

To determine when the balance will exceed $500, we can use the compound interest formula:

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

Where:

A is the balance after time t

P is the principal amount, which is $400 in this case

r is the interest rate, which is 2.4%

n is the number of times the interest is compounded per year, which is 12 (monthly)

t is the number of years

Let's solve for t when the balance exceeds $500:

$500 = $400(1 + 0.024/12)^(12t)

Divide both sides by $400:

1.25 = (1.002)^12t

Take the natural logarithm of both sides:

ln(1.25) = ln((1.002)^12t)

Using logarithm properties, we can simplify the equation:

12t = ln(1.25)/ln(1.002)

Finally, solve for t:

t = ln(1.25)/ln(1.002) / 12

Using a calculator, we find that t is approximately 2.08 years. So, the balance will first exceed $500 after approximately 2 years and 1 month.

Answer 2

The answer is $88

Step-by-step explanation:

The Math.random () function returns a floating-point, pseudo-random number in the range 0–1 (inclusive of 0, but not 1) with approximately uniform distribution over that range — which you can then scale to your desired range.