On January 1st, 2019 you put $1000 into an account growing at 2% APR compounded daily. Starting that same day, you invest $10/week into an account paying 3% compounded weekly. Write down the formula for the total value of your investments exactly one year (365 days) later.

2. Suppose a deposit of R dollars is made at the end of each year, and assume an APR of r% compounding continuously.

(a) If we invest like this for 3 years, what is the value of the account after the third year?

(b) If we are making these payments for 3 years, how much money must we invest today to cover the payments?

(c) If we make these payments in perpetuity, find a formula which describes the amount of principal we must invest today to cover all future payments.

(d) If we invest like this for three years, but instead use an account with an APR s% compounded weekly, determine s so that this second account has the same value as your answer in part (a) after three years.

3. Suppose an ordinary annuity consists of $100 deposits made every week at an APR of 3%, compounding weekly. Use sigma notation to write down the future value of the annuity after 1 year.

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1 Formula for the total value of investments after one year Let P1 be the initial principal of 1000 r1 be the annual interest rate of 2 compounded dai... View the full answer