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.### Rebecca's initial investment of \frac{0.0375}{12} = 0.003125 FV = PV(1 + r)^n FV PV r n FV = 1000(1 + 0.003125)^{10} \approx 1031.56 2000 by next summer. Since her initial investment will grow to approximately 2000 - 1031.56 = 968.44 968.44 over 10 months. Let be the monthly deposit. The future value of an ordinary annuity is given by , where is the future value, is the monthly payment, is the monthly interest rate, and is the number of months. In this case, the monthly interest rate is . We have . Solving for , we get .