Math / Numbers & Operations

QuestionHow much interest is earned on a CD with a 2 year fixed maturity, if the initial investment is $\$ 810$ and the annual interest rate is $2.3 \%$ ?

Studdy Solution

STEP 1

1. The interest is compounded annually.
2. The initial investment is \$810.
3. The annual interest rate is 2.3%.
4. The maturity period is 2 years.
\

STEP 2

1. Calculate the amount of money after the first year by applying the annual interest rate.
2. Calculate the amount of money after the second year by applying the annual interest rate to the amount after the first year.
3. Subtract the initial investment from the final amount to find the earned interest.
\_STEP_1_: High\_Level\_Step: 1
Calculate the amount of money after the first year using the formula: $A_1 = P \left(1 + \frac{r}{100}\right)$ where $P$ is the initial investment, $r$ is the annual interest rate, and $A_1$ is the amount after the first year.
$A_1 = 810 \left(1 + \frac{2.3}{100}\right)$
High\_Level\_Step\_Completed: FALSE
\_STEP_2_: High\_Level\Step: 1
Simplify the expression and solve for $A_1$ :
$A_1 = 810 \left(1 + 0.023\right)$ $A_1 = 810 \times 1.023$ $A_1 = 828.63$
High\_Level\_Step\_Completed: TRUE
\_STEP_3_: High\_Level\_Step: 2
Calculate the amount of money after the second year using the formula: $A_2 = A_1 \left(1 + \frac{r}{100}\right)$ where $A_2$ is the amount after the second year.
$A_2 = 828.63 \left(1 + \frac{2.3}{100}\right)$
High\_Level\_Step\_Completed: FALSE
\_STEP_4_: High\_Level\_Step: 2
Simplify the expression and solve for $A_2$ :
$A_2 = 828.63 \left(1 + 0.023\right)$ $A_2 = 828.63 \times 1.023$ $A_2 = 847.64$
High\_Level\_Step\_Completed: TRUE
\_STEP_5_: High\_Level\_Step: 3
Calculate the interest earned by subtracting the initial investment from the final amount:
$\text{Interest Earned} = A_2 - P$ $\text{Interest Earned} = 847.64 - 810$ $\text{Interest Earned} = 37.64$
High\_Level\_Step\_Completed: TRUE
The interest earned on the CD after 2 years is \$37.64.
END\_OF\_SOLUTION

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