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QuestionWhat is the balance after 15 years for a \1500depositata71500 deposit at a 7% quarterly compounded interest rate? Use F=P(1+\frac{r}{n})^{nt}.Enter. Enter P=\[?][?]

Studdy Solution

STEP 1

Assumptions1. The initial deposit (principal) is 1500.Theinterestrateis71500. The interest rate is7%<br />3. The interest is compounded quarterly4. The time for the investment is15 years5. The formula for compound interest is given by=P(1+rn)nt=P\left(1+\frac{r}{n}\right)^{n t}where−where - isthefuturevalueoftheinvestment/loan,includinginterest− is the future value of the investment/loan, including interest - istheprincipalinvestmentamount(theinitialdepositorloanamount)− is the principal investment amount (the initial deposit or loan amount) - ristheannualinterestrate(indecimalform)− is the annual interest rate (in decimal form) - nisthenumberoftimesthatinterestiscompoundedperyear− is the number of times that interest is compounded per year - t$ is the time the money is invested for in years

STEP 2

First, we need to convert the interest rate from a percentage to a decimal. This can be done by dividing the interest rate by100.
r=7%100r = \frac{7\%}{100}

STEP 3

Calculate the decimal value of the interest rate.
r=7100=0.07r = \frac{7}{100} =0.07

STEP 4

Now, we can plug in the given values into the compound interest formula.
=$1500(1+0.074)4×15 = \$1500 \left(1+\frac{0.07}{4}\right)^{4 \times15}

STEP 5

Calculate the value inside the parentheses.
1+0.074=1.01751 + \frac{0.07}{4} =1.0175

STEP 6

Substitute the calculated value back into the formula.
=$1500×(1.0175)4×15 = \$1500 \times (1.0175)^{4 \times15}

STEP 7

Calculate the exponent.
4×15=604 \times15 =60

STEP 8

Substitute the calculated value back into the formula.
=$1500×(1.0175)60 = \$1500 \times (1.0175)^{60}

STEP 9

Calculate the future value of the investment.
=$150×(.0175)60≈$4173.19 = \$150 \times (.0175)^{60} \approx \$4173.19The balance after15 years is approximately $4173.19.

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