a customer deposits $500 in an account that pays 4% annual interest. what is the balance after 3 years if…

a customer deposits $500 in an account that pays 4% annual interest. what is the balance after 3 years if the interest is compounded annually?\ncompound interest formula: $v(t)=p(1 + \\frac{r}{n})^{nt}$\nt = years since initial deposit\nn = number of times compounded per year\nr = annual interest rate (as a decimal)\np = initial (principal) investment\nv(t) = value of investment after t years\n$500.12\n$512.00\n$560.00\n$562.43

a customer deposits $500 in an account that pays 4% annual interest. what is the balance after 3 years if the interest is compounded annually?\ncompound interest formula: $v(t)=p(1 + \\frac{r}{n})^{nt}$\nt = years since initial deposit\nn = number of times compounded per year\nr = annual interest rate (as a decimal)\np = initial (principal) investment\nv(t) = value of investment after t years\n$500.12\n$512.00\n$560.00\n$562.43

Answer

Explanation:

Step1: Identify the values

$P = 500$, $r=0.04$, $n = 1$, $t = 3$

Step2: Substitute into formula

$V(t)=P(1 +\frac{r}{n})^{nt}=500(1+\frac{0.04}{1})^{1\times3}$

Step3: Calculate the exponent part

$(1 + 0.04)^{3}=1.04^{3}=1.04\times1.04\times1.04 = 1.124864$

Step4: Calculate the final value

$V(t)=500\times1.124864 = 562.432\approx562.43$

Answer:

$562.43$