Question

you deposit $400 in an account that pays 6% interest compounded semiannually. after 5 years, the interest rate is increased to 6.12% compounded quarterly. what will be the value of the account after a total of 10 years? click the icon to view some finance formulas. the value of the account will be $□ (round to the nearest dollar as needed.)

Explanation:

Step1: Calculate amount for first 5 - year period

The compound - interest formula is $A = P(1+\frac{r}{n})^{nt}$, where $P$ is the principal amount, $r$ is the annual interest rate (in decimal), $n$ is the number of times interest is compounded per year, and $t$ is the number of years. For the first 5 years, $P = 400$, $r=0.06$, $n = 2$ (semi - annually), and $t = 5$.
$A_1=400(1 +\frac{0.06}{2})^{2\times5}=400(1 + 0.03)^{10}$
$A_1=400\times1.03^{10}\approx400\times1.343916379\approx537.5665516$

Step2: Calculate amount for second 5 - year period

This $A_1$ becomes the principal for the next 5 - year period. Now, $r = 0.0612$, $n=4$ (quarterly), and $t = 5$.
$A=A_1(1+\frac{0.0612}{4})^{4\times5}=537.5665516(1 + 0.0153)^{20}$
$(1 + 0.0153)^{20}\approx1.357911797$
$A=537.5665516\times1.357911797\approx729$

Answer:

729