if $1250 are deposited into an account with a 8% interest rate, compounded quarterly, what is the balance…

if $1250 are deposited into an account with a 8% interest rate, compounded quarterly, what is the balance after 15 years? f = $? f = p(1 + \\frac{r}{n})^{nt} round to the nearest cent.

if $1250 are deposited into an account with a 8% interest rate, compounded quarterly, what is the balance after 15 years? f = $? f = p(1 + \\frac{r}{n})^{nt} round to the nearest cent.

Answer

Explanation:

Step1: Identify the values of P, r, n, t

$P = 1250$ (principal amount), $r=0.08$ (annual interest rate), $n = 4$ (compounding times per year), $t = 15$ (number of years)

Step2: Substitute values into the compound - interest formula

$F=P(1 +\frac{r}{n})^{nt}=1250(1+\frac{0.08}{4})^{4\times15}$

Step3: Calculate the value inside the parentheses

$1+\frac{0.08}{4}=1 + 0.02=1.02$

Step4: Calculate the exponent

$nt=4\times15 = 60$

Step5: Calculate the value of $(1.02)^{60}$

Using a calculator, $(1.02)^{60}\approx3.281030795$

Step6: Calculate the final amount F

$F=1250\times3.281030795\approx4101.29$

Answer:

$4101.29$