Question

Jack and Collin each deposit $17,250 into accounts that earn 6% interest for 6.5 years. Jack’s account earns annual simple interest and Collin's account earns annual compound interest. Who will earn more interest after 6 years, and how much more interest will they earn?

Answer 1

Answer: For Jack's account, we can use the formula for simple interest:

I = P * r * t

where I is the interest earned, P is the principal (initial deposit), r is the interest rate, and t is the time in years.

So for Jack's account, we have:

I = 17250 * 0.06 * 6.5 = $6,682.50

For Collin's account, we can use the formula for compound interest:

A = P * (1 + r/n)^(n*t)

where A is the amount after t years, P is the principal (initial deposit), r is the interest rate, n is the number of times interest is compounded per year, and t is the time in years.

In this case, we know that Collin's account earns annual compound interest, so n = 1.

So for Collin's account, we have:

A = 17250 * (1 + 0.06/1)^(1*6.5) = $25,344.55

The interest earned on Collin's account is the difference between the amount after 6.5 years and the initial deposit:

I = 25344.55 - 17250 = $8,594.55

Therefore, Collin will earn more interest than Jack, and the difference is:

$8,594.55 - $6,682.50 = $1,912.05

So Collin will earn $1,912.05 more interest than Jack after 6 years.

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