Question

Samuel wants to deposit $4,000 and keep that money in the bank without deposits or

withdrawals for three years. He compares two different options. Option 1 will pay 3.8%
interest, compounded quarterly. Option 2 will pay 3.5% interest, compounded
continuously.
a. How much interest does Option 1 pay?
b. How much interest does Options 2 pay?

Answer 1

For Option 1, the interest paid is $404.81. For Option 2, the interest paid is $441.57.

Step-by-step explanation:

For Option 1, the interest is compounded quarterly.

To calculate the interest, we use the formula
`A = P(1 + r/n)^(nt)`

where A is the final amount, P is the principal amount, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years.

In this case, P = $4,000, r = 3.8% or 0.038, n = 4 (quarterly compounding), and t = 3 years.

Plugging these values into the formula, we get

`A = $4,000(1 + 0.038/4)^(4 * 3)`

= $4,404.81.

The interest paid is $4,404.81 - $4,000 = $404.81.

For Option 2, the interest is compounded continuously.

To calculate the interest, we use the formula A = P*e^(rt), where e is Euler's number( approximately 2.71828).

In this case, P = $4,000, r = 3.5% or 0.035, and t = 3 years.

Plugging these values into the formula, we get

`A = $4,000 * e^(0.035 * 3)`

= $4,441.57.

The interest paid is $4,441.57 - $4,000 = $441.57.

Answer 2

Step-by-step explanation:

$4,182.71

Step-by-step explanation:

$182.71 will be added in interest after 3 years.