Question

If you had $500 to put into a savings account with 8% interest , how would you know which bank to choose, if you plan to withdraw everything after 10 years—one that pays simple interest or compound interest? Explain.

Answer 1

Since you would withdraw more money with the compound interest, you would choose the bank which uses compund interest.

Explanation:

Simple interest formula:

The simple interest formula is given by:

`E = P*r*t`

In which E are the earnings, P is the principal(the initial amount of money), r is the interest rate(yearly, as a decimal) and t is the time.

After t years, the total amount of money is:

`T = E + P`.

Compound interest formula:

The compound interest formula is given by:

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

Where A is the amount of money, 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 unit t and t is the time the money is invested or borrowed for.

In this problem:

`P = 500, r = 0.08, t = 10`

So

Simple interest:

`E = P*r*t = 500*0.08*10 = 400`

In total:

`T = E + P = 500 + 400 = 900`

Using simple interest, you would withdraw an amount of $900.

Compound interest

We use n = 1

`A = P(1 + (r)/(n))^(nt) = 500(1 + (0.08)/(1))^(10) = 1079.46`

You would withdraw $1079.86. Since you would withdraw more money with the compound interest, you would choose the bank which uses compund interest.