QuestionAustin invests \$1554 quarterly at 2% interest, compounded quarterly. Find the annuity's value after 3 years.

Studdy Solution

STEP 1

Assumptions1. Austin is buying an annuity with quarterly payments. . The interest rate is% compounded quarterly.
3. Payments will be made at the end of each quarter.
4. The time for the annuity is3 years.
5. Each quarterly payment is $1554.

STEP 2

First, we need to find the number of quarters in years. $Number\, of\, quarters = Number\, of\, years \\times4$

STEP 3

Now, plug in the given value for the number of years to calculate the number of quarters.
$Number\, of\, quarters =3 \\times$

STEP 4

Calculate the number of quarters.
$Number\, of\, quarters =3 \\times4 =12$

STEP 5

We need to calculate the future value of the annuity. The formula for the future value of an annuity, when payments are made at the end of each period, is given by $V = \times \left( \frac{(1 + r)^n -1}{r} \right)$ where- $V$ is the future value of the annuity- $$ is the payment per period- $r$ is the interest rate per period- $n$ is the number of periods

STEP 6

Now, plug in the given values for the payment per period, the interest rate per period, and the number of periods to calculate the future value.
$V = \$1554 \times \left( \frac{(1 +0.02)^{12} -1}{0.02} \right)$

STEP 7

Calculate the future value of the annuity.
$V = \$1554 \times \left( \frac{(1 +0.02)^{12} -1}{0.02} \right) = \$20,563.34$ Austin's annuity will be worth $20,563.34 in3 years.

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