A mother invests $7000 in a bank account at the time of her daughter's birth. The interest is 18) compounded quarterly at a rate

Question

2 years ago

5

A mother invests $7000 in a bank account at the time of her daughter's birth. The interest is 18) compounded quarterly at a rate

of 8%. What will be the value of the daughter's account on her twentieth birthday, assuming no other deposits or withdrawals are made during this period?

Mathematics

1 answer:

Alex · Answer 1 · 2023-06-23T23:32:31+03:00

Alex2 years ago

5 0

well, from birth to your twentieth birthday that'll just be 20 years, so

$~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$7000\\ r=rate\to 8\%\to \frac{8}{100}\dotfill &0.08\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &20 \end{cases} \\\\\\ A=7000\left(1+\frac{0.08}{4}\right)^{4\cdot 20}\implies A=7000(1.02)^{80}\implies A\approx 34128.07$