diane is saving up money to buy a car. diane puts $8,000.00 into an account which earns 2% interest…

diane is saving up money to buy a car. diane puts $8,000.00 into an account which earns 2% interest, compounded annually. how much will she have in the account after 4 years? use the formula $a = p(1+\frac{r}{n})^{nt}$, where $a$ is the balance (final amount), $p$ is the principal (starting amount), $r$ is the interest rate expressed as a decimal, $n$ is the number of times per year that the interest is compounded, and $t$ is the time in years. round your answer to the nearest cent.

diane is saving up money to buy a car. diane puts $8,000.00 into an account which earns 2% interest, compounded annually. how much will she have in the account after 4 years? use the formula $a = p(1+\frac{r}{n})^{nt}$, where $a$ is the balance (final amount), $p$ is the principal (starting amount), $r$ is the interest rate expressed as a decimal, $n$ is the number of times per year that the interest is compounded, and $t$ is the time in years. round your answer to the nearest cent.

Answer

Explanation:

Step1: Identify the values

$P = 8000$, $r=0.02$, $n = 1$, $t = 4$

Step2: Substitute values into formula

$A=P(1 +\frac{r}{n})^{nt}=8000\times(1+\frac{0.02}{1})^{1\times4}$

Step3: Calculate the exponent part

$(1 + 0.02)^{4}=1.02^{4}=1.08243216$

Step4: Calculate the final amount

$A = 8000\times1.08243216=8659.45728\approx8659.46$

Answer:

$8659.46$