Question

An employee wants to invest ​$50,000 in a pension plan. One investment offers 4​% compounded quarterly. Another offers 3.75​% compounded continuously.
​(a) Which investment will earn more interest in 4 ​yr?
​(b) How much more will the better plan​ earn?

Answer 1

Using compound interest and continuous compouding, it is found that:

a) The investment at 4% compounded quarterly will earn more interest in 4 years.

b) The better plan will earn $537 more.

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.

In this problem, the parameters are: P = 50000, r = 0.04, n = 4, t = 4, hence the amount will be of:

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

$A(4) = 50000\left(1 + \frac{0.04}{4}\right)^{4 \times 4}$

A(4) = $58,629.

What is the continuous compounding formula?

It is given by:

$A(t) = Pe^{rt}$

In this problem, this option has r = 0.0375, hence:

$A(4) = 50000e^{0.0375 \times 4} = 58092$

Then:

Item a:

The investment at 4% compounded quarterly will earn more interest in 4 years.

Item b:

58629 - 58092 = $537.

The better plan will earn $537 more.

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