Question

How much do you need to invest in an account earning an annual interest rate of 2.938% compounded weekly, so that your money will grow to $7,880.00 in 50 weeks?

Answer 1

Bearing in mind the compounding is weekly on an APR, so the compounding cycle is 52, since there are 52 weeks in a year

however, the maturity term in years, is just 50/52, since is 50weeks from 52 in a year, so is 50/52 years, which is just a fraction of a year

$\bf \qquad \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\to &\ 7,880\\ P=\textit{original amount deposited}\\ r=rate\to 2.938\%\to \frac{2.938}{100}\to &0.02938\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{weekly, thus fifty two} \end{array}\to &52\\ t=years\to \frac{50}{52}\to &\frac{25}{26} \end{cases} \\\\\\ 7880=P\left(1+\frac{0.02938}{52}\right)^{52\cdot \frac{25}{26}}$

solve for P