Question

Moira can invest $10,000 in an account at Bank A that earns 4% interest compounded monthly or she can investm at Bank B at a rate of 8% compounded semiannually. Which is the first account to reach $20,000? Justify your answer.

Answer 1

Bank A will reach $20,000 first in approximately 13.6 years, compared to Bank B's 9.50 years.

Step-by-step explanation:

To find out which account will reach $20,000 first, let's calculate the future value of each account.

For Bank A, the formula for calculating the future value of an investment with compound interest is:

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

V = future value, P = principal amount, r = annual interest rate, n = number of times compounded per year, and t = number of years.

In this case, P = $10,000, r = 4% or 0.04, n = 12 (compounded monthly), and we want to find the value of t when V = $20,000.

So:

$20,000 = $10,000(1 + 0.04/12)^(12t)

To solve for t, we can use logarithms or trial and error.

After evaluating, we find that t is approximately 13.6 years.

For Bank B, the formula is slightly different because interest is compounded semiannually:

$20,000 = $10,000(1 + 0.08/2)^(2t)

Solving for t, we find that t is approximately 9.50 years.

Therefore, Bank A will reach $20,000 first, in approximately 13.6 years compared to Bank B's 9.50 years.