mandy has $6,118 in an account. the interest rate is 9 3/4% compounded annually. to the nearest cent, how…

mandy has $6,118 in an account. the interest rate is 9 3/4% compounded annually. to the nearest cent, how much will she have in 5 years? use the formula b = p(1 + r)^t, where b is the balance (final amount), p is the principal (starting amount), r is the interest rate expressed as a decimal, and t is the time in years.

mandy has $6,118 in an account. the interest rate is 9 3/4% compounded annually. to the nearest cent, how much will she have in 5 years? use the formula b = p(1 + r)^t, where b is the balance (final amount), p is the principal (starting amount), r is the interest rate expressed as a decimal, and t is the time in years.

Answer

Explanation:

Step1: Convert interest rate to decimal

$r = 9\frac{3}{4}%=\frac{9.75}{100}=0.0975$

Step2: Identify principal and time

$p = 6118$, $t = 5$

Step3: Substitute values into formula

$B=p(1 + r)^t=6118\times(1 + 0.0975)^5$

Step4: Calculate $(1 + 0.0975)^5$

$(1 + 0.0975)^5=1.0975^5\approx1.59092$

Step5: Calculate final amount

$B = 6118\times1.59092\approx9733.25$

Answer:

$9733.25$