Question

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2. Jerry has two choices, one is depositing $3,000 in a certificate of deposit that pays 2.8% interest,

compounded annually for 4 years. The other is depositing $3,000 at 2.8% with simple interest for 4 years.

Which is better and by how much?

Answer 1

Compound interest is better, by $14.36.

Explanation:

Simple Interest:

The simple interest formula is given by:

`E = P*I*t`

In which E is the amount of interest earned, P is the principal(the initial amount of money), I 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:

The compound interest formula is given by:

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

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

Total amount in compound interest:

$3,000 in a certificate of deposit that pays 2.8% interest, compounded annually for 4 years. This means, respectively, that
`P = 3000, r = 0.028, n = 1, t = 4`

So

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

`A(4) = 3000(1 + (0.028)/(1))^(4) = 3350.38`

Total amount in simple interest:

`P = 3000, I = 0.028, t = 4`

So

`E = P*I*t = 3000*0.028*4 = 336`

`T = E + P = 3000 + 336 = 3336`

Which is better and by how much?

Higher earning with compound interest, so it is better.

3350.36 - 3336 = 14.36

Compound interest is better, by $14.36.