Question

Jack was given $3520 from his grandma, and decides to put the money into an account that has a 6.5% interest rate that is compounded annually.

Describe the type of equation that models Jack’s situation. Create that equation of Jack’s situation. Using the equation you created, how much money will be in Jack’s account after 3 years? How much will be in his account after 10 years?

Answer 1

Using compound interest, it is found that:

• The equation is: $A(t) = 3520(1.065)^t$

• After 3 years, he has $4,252 in the account.

• After 10 years, he has $6,608 in the account.

What is compound interest?

The amount of money earned, in compound interest, after t years, is given by:

$A(t) = P\left(1 + \frac{r}{n}\right)^{nt}$

In which:

• A(t) is the amount of money after t years.

• P is the principal(the initial sum of money).

• r is the interest rate(as a decimal value).

• n is the number of times that interest is compounded per year.

• t is the time in years for which the money is invested or borrowed.

In this problem:

• Jack was given $3520 from his grandma, hence P = 3520.

• The account pays 6.5% interest rate that is compounded annually, hence n = 1, r = 0.065.

Hence, the equation is:

$A(t) = P\left(1 + \frac{r}{n}\right)^{nt}$

$A(t) = 3520\left(1 + \frac{0.065}{1}\right)^{t}$

$A(t) = 3520(1.065)^t$

After 3 and 10 years, respectively, the amount in dollars in the account are given by:

$A(3) = 3520(1.065)^3 = 4252$

$A(10) = 3520(1.065)^{10} = 6608$

More can be learned about compound interest at https://brainly.com/question/25781328