investing $10,000 in a savings account at 3% annual interest compounded monthly will result in approximately…

investing $10,000 in a savings account at 3% annual interest compounded monthly will result in approximately how much money after 10 years? use the formula: $a = p(1+\frac{r}{n})^{nt}$. $10,564.68 $13,000.00 $13,493.54 $13,439.16

investing $10,000 in a savings account at 3% annual interest compounded monthly will result in approximately how much money after 10 years? use the formula: $a = p(1+\frac{r}{n})^{nt}$. $10,564.68 $13,000.00 $13,493.54 $13,439.16

Answer

Explanation:

Step1: Identify values for formula

$P = 10000$ (principal amount), $r=0.03$ (annual interest rate as a decimal), $n = 12$ (number of times compounded per year), $t = 10$ (number of years).

Step2: Substitute values into formula

$A=P(1 +\frac{r}{n})^{nt}=10000(1+\frac{0.03}{12})^{12\times10}$

Step3: Calculate inside the parentheses first

$1+\frac{0.03}{12}=1 + 0.0025=1.0025$

Step4: Calculate the exponent

$nt=12\times10 = 120$

Step5: Calculate the power

$(1.0025)^{120}\approx1.349354$

Step6: Calculate the final amount

$A = 10000\times1.349354=13493.54$

Answer:

$13,493.54$