Question

Linda invests $3000 in a bond trust that pays 8% interest compounded monthly. Her friend Lyla invests $3000 in a certificate of deposit that pays 7.75% compounded continuously. For Linda: a. State which formula should be used to solve this problem. _____________________ b. Write the function for Linda. _____________________ c. Determine how much Linda would have in her account after 20 years

Answer 1

Answer:

a) The interest is compounded monthly, so should use the compound interest formula.

b) $A(t) = 3000(1.0067)^{12t}$

c) Linda would have $14898.33 in her account after 20 years.

Step-by-step explanation:

Compound Interest Formula:

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

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 number of years for which the money is invested.

Continuous Interest Formula:

$P(t) = P(0)e^{rt}$

In which P(0) is the initial amount invested and r is the interest rate, as a decimal.

For Linda: a. State which formula should be used to solve this problem.

The interest is compounded monthly, so should use the compound interest formula.

b. Write the function for Linda.

Invests 3000, so $P = 3000$

8% interest, so $r = 0.08$

Compounded monthly. An year has 12 months, so $n = 12$

Then

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

$A = 3000(1 + \frac{0.08}{12})^{12t}$

$A = 3000(1.0067)^{12t}$

c. Determine how much Linda would have in her account after 20 years

This is A(20)

$A = 3000(1.0067)^{12*20} = 14898.33$

Linda would have $14898.33 in her account after 20 years.