tallulah invested $70,000 in an account paying an interest rate of 5.2% compounded quarterly. assuming no…

Explanation:

Step1: Identify the compound - interest formula

The compound - interest formula is $A = P(1+\frac{r}{n})^{nt}$, where $A$ is the amount of money in the account after $t$ years, $P$ is the principal amount (initial investment), $r$ is the annual interest rate (in decimal form), $n$ is the number of times interest is compounded per year, and $t$ is the number of years.

Step2: Convert the given values to the appropriate form

We are given that $P=$70000$, $r = 5.2%=0.052$, $n = 4$ (compounded quarterly), and $t = 13$ years.

Step3: Substitute the values into the formula

$A=70000(1 +\frac{0.052}{4})^{4\times13}$ First, calculate the value inside the parentheses: $\frac{0.052}{4}=0.013$, and $1 + 0.013=1.013$. Then, calculate the exponent: $4\times13 = 52$. So, $A = 70000\times(1.013)^{52}$.

Step4: Calculate $(1.013)^{52}$

Using a calculator, $(1.013)^{52}\approx1.9777$.

Step5: Calculate the value of $A$

$A=70000\times1.9777 = 138439$.

Answer:

$138439$