Question

Lydia invests $1,100 in an account that earns interest at an annual rate of 5.5% compounded monthly.What is Lydia's return on investment after 2 years?

Answer 1

Lydia's return on investment after 2 years is approximately $1,222.25

Step-by-step explanation:

To find Lydia's return on investment after 2 years, we can use the formula for compound interest:

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

Where:

• A is the final amount
• P is the principal amount (initial investment)
• r is the annual interest rate (in decimal form)
• n is the number of times the interest is compounded per year
• t is the number of years

In this case, Lydia invests $1,100 at an annual interest rate of 5.5%, which is compounded monthly (so n = 12). The investment period is 2 years (so t = 2).

Substituting these values into the formula, we get:

A = $1,100(1 + 0.055/12)^(12 * 2)

Simplifying this equation, we find that Lydia's return on investment after 2 years is approximately $1,222.25.

Answer 2

The rule of the compounded interest is

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

A is the new amount

P is the initial amount

r is the interest rate in decimal

n is the number of periods per year

t is the number of years

Since the initial amount is $1100, then

P = 1100

Since the interest rate is 5.5%, then

`r=(5.5)/(100)=0.055`

r = 0.055

Since the interest is compounded monthly, then

n = 12

Since the time is 2 years, then

t = 2

Substitute them in the rule above to find A

`\begin{gathered} A=1100(1+(0.055)/(12))^(12*2) \\ A=1100(1+(11)/(2400))^(24) \\ A=1227.597324 \end{gathered}`

Lydia's return after 2 years is $1227.60 to the nearest cent