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+(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 (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 (50)/(52)\to &(25)/(26) \end{cases} \\\\\\ 7880=P\left(1+(0.02938)/(52)\right)^{52\cdot (25)/(26)}`

solve for P