Fractions and Decimals

Discrete Mathematics

Differential Equations

Solved on Nov 20, 2023

Find the final amount for a $19,000 deposit at 7% annual interest, compounded quarterly, after 9 years. (Round to nearest cent)
$\$ 29,652.06$

STEP 1

Assumptions1. The initial deposit amount is \$19,000. The annual interest rate is7%
3. The compounding frequency is quarterly (4 times a year)
4. The time for compounding is9 years5. The compound amount is calculated using the formula for compound interest

STEP 2

The formula for compound interest is given by $A = \left(1 + \frac{r}{n}\right)^{nt}$ where- A is the amount of money accumulated after n years, including interest. - is the principal amount (the initial amount of money). - r is the annual interest rate (in decimal form). - n is the number of times that interest is compounded per year. - t is the time the money is invested for, in years.

STEP 3

First, we need to convert the annual interest rate from a percentage to a decimal. $7\% =0.07$

STEP 4

Now, plug in the given values for (the initial deposit), r (the annual interest rate in decimal form), n (the number of times interest is compounded per year), and t (the time the money is invested for in years) into the formula.
$A = \$19,000 \left(1 + \frac{0.07}{4}\right)^{4 \times9}$

STEP 5

Calculate the compound amount.
$A = \$19,000 \left(1 + \frac{0.07}{4}\right)^{4 \times9}$

STEP 6

Round the compound amount to the nearest cent.
The compound amount after9 years will be \$\square.

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