Client $1,$

Your client wants to know how much she needs to invest this year so that her sister's new child will have $$30,000$ on their ${18}^{th}$ birthday. You tell her you have a product that will accomplish this, it compounds interest monthly, at $5\mathrm{.}5\%$ interest for $18$ years, in other words in the compound interest formula you know, $A=$ $$30,000,n=12,r=0\mathrm{.}055,$ and $t=18.$ Plug these values into the formula and solve for $P$ the amount needed to invest to accomplish her goal. In other words for the compound interest formula $A=P(1+\frac{r}{n}{)}^{nt}$ solve for $P$ and get, $P=\frac{A}{(1+\frac{r}{n}{)}^{nt}}.$ Use the second formula to find P$.$

Client $2.$

Your second client wants to know how long it will take for his $$150,000$ machine will depreciate to $$75,000$ if it decreases in value at a rate of $7\mathrm{.}7\%$ per year. Use the formula,

$A=P{e}^{-0\mathrm{.}077t}$ and logs to solve for $t$