Question

ivan is saving up money to buy a car. ivan puts $6,049.00 into an account which earns 9% interest, compounded monthly. how much will he have in the account after 2 years? use the formula $a = p\left(1 + \frac{r}{n}\
ight)^{nt}$, 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.

Explanation:

Step1: Identify given values

$P = 6049$, $r = 0.09$, $n = 12$, $t = 2$

Step2: Calculate $\frac{r}{n}$

$\frac{0.09}{12} = 0.0075$

Step3: Calculate $nt$

$12 \times 2 = 24$

Step4: Compute $(1+\frac{r}{n})^{nt}$

$(1 + 0.0075)^{24} = (1.0075)^{24} \approx 1.1964135$

Step5: Calculate final amount $A$

$A = 6049 \times 1.1964135$

Answer:

$\$7237.10$