lashonda has decided to invest to help with her retirement savings. how much would she have to invest to…

Explanation:

Step1: Identify the compound - interest formula

The compound - interest formula for the future value $A$ is $A = P(1+\frac{r}{n})^{nt}$, where $A$ is the future value, $P$ is the principal amount (the initial investment we want to find), $r$ is the annual interest rate (as a decimal), $n$ is the number of times interest is compounded per year, and $t$ is the number of years. We are given that $A=$136900$, $r = 0.0356$ (since $3.56%=0.0356$), $n = 12$ (compounded monthly), and $t = 16$ years. We need to solve the formula for $P$: $P=\frac{A}{(1 +\frac{r}{n})^{nt}}$.

Step2: Substitute the values into the formula

First, calculate the exponent $nt$: $nt=12\times16 = 192$. Then, calculate $\frac{r}{n}$: $\frac{r}{n}=\frac{0.0356}{12}$. Next, calculate $(1+\frac{r}{n})^{nt}=(1 +\frac{0.0356}{12})^{192}$. $(1+\frac{0.0356}{12})\approx1+\ 0.002967=1.002967$. $(1.002967)^{192}\approx1.7997$. Finally, calculate $P$: $P=\frac{136900}{(1+\frac{0.0356}{12})^{192}}=\frac{136900}{1.7997}\approx76077$.

Answer:

$$76077$