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QuestionCalculate Mario's savings after 10 years with \1000at4%interestusing1000 at 4\% interest using A=p(1+r)^{t}$. Options: a. \$2156.01 b. \$1004 c. \$1000 d. \$1428.24

Studdy Solution

STEP 1

Assumptions1. The initial amount (p) Mario puts into the savings account is 1000..Theannualinterestrate(r)is41000. . The annual interest rate (r) is4%.<br />3. The time (t) for which the money is deposited is10 years.<br />4. The interest is compounded annually.<br />5. The formula for compound interest is A=p(1+r)^{t}$, where A is the final amount, p is the principal amount, r is the interest rate, and t is the time in years.

STEP 2

First, we need to convert the interest rate from a percentage to a decimal. We can do this by dividing the interest rate by100.
r=Interest rate100r = \frac{Interest\, rate}{100}

STEP 3

Now, plug in the given value for the interest rate to calculate r.
r=%100r = \frac{\%}{100}

STEP 4

Calculate the interest rate in decimal form.
r=4100=0.04r = \frac{4}{100} =0.04

STEP 5

Now that we have the interest rate in decimal form, we can plug in the values into the compound interest formula to calculate the final amount.
A=p(1+r)tA = p(1+r)^{t}

STEP 6

Plug in the values for p, r, and t into the formula.
A=$1000(1+0.04)10A = \$1000(1+0.04)^{10}

STEP 7

Calculate the value inside the parentheses.
1+0.04=1.041+0.04 =1.04So, the formula becomesA=$1000(1.04)10A = \$1000(1.04)^{10}

STEP 8

Calculate the final amount A.
A=$1000(1.04)10=$1480.24A = \$1000(1.04)^{10} = \$1480.24Mario will have $1480.24 after10 years.

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