Rebecca saved 1000 from her summer job and bought a CSB earning 3.75% compounded monthly. She started an after school job in September and wants to have 2000 by next summer so she can go travelling. How much does she need to save from her pay every month for 10 months if she can deposit the money in an account earning 2% , compounded monthly?

## Step 1: Calculate the future value of the initial investment.<br />### Rebecca's initial investment of $1000 grows at an annual interest rate of 3.75% compounded monthly for 10 months. The monthly interest rate is $\frac{0.0375}{12} = 0.003125$. The future value after 10 months is given by the formula $FV = PV(1 + r)^n$, where $FV$ is the future value, $PV$ is the present value, $r$ is the monthly interest rate, and $n$ is the number of months. Therefore, $FV = 1000(1 + 0.003125)^{10} \approx 1031.56$.<br /><br />## Step 2: Calculate the remaining amount needed.<br />### Rebecca wants to have $2000 by next summer. Since her initial investment will grow to approximately $1031.56, she needs to save an additional $2000 - 1031.56 = 968.44$.<br /><br />## Step 3: Calculate the monthly savings required.<br />### Rebecca needs to save $968.44 over 10 months. Let $P$ be the monthly deposit. The future value of an ordinary annuity is given by $FV = P \frac{(1+r)^n - 1}{r}$, where $FV$ is the future value, $P$ is the monthly payment, $r$ is the monthly interest rate, and $n$ is the number of months. In this case, the monthly interest rate is $\frac{0.02}{12} \approx 0.001667$. We have $968.44 = P \frac{(1+0.001667)^{10} - 1}{0.001667}$. Solving for $P$, we get $P \approx \frac{968.44}{10.0083} \approx 96.76$.