Assume compounded interest for all problems. Use an Excel formula that shows the variables inside or identify the type of problem and list the variables used to solve the problem (e.g. PVOA, n=20, i=2, pmt=$100, etc.)

1. How much will you have in the bank if you deposit $1,100 at the end of each of the next 12 months and the bank is paying 12 percent APR, compounded monthly?

2. How much do you need to deposit in the bank now if you want to withdraw a lump sum of $12,000 in 8 years and you will be earning 7 percent APR, compounded annually?

3. Since finances are tight, you are having a hard time paying for your child’s private education. Fortunately, your well-to-do granddad wants to help. How much should he deposit in a bank now in order to have enough to withdraw $1,100 at the beginning of each of the next 10 years, assuming a constant rate of 8% APR, compounded annually? (The first withdrawal occurs today.)

4. Assume that Bank of America pays 6% APR on its certificates of deposit (CD), compounded semi-annually. Down the street, Savers Credit Union pays 6% APR on its CDs, compounded quarterly. Calculate the effective annual rate for (a) Bank of America, and (b) Savers Credit Union.

5. (a) Use the Rule of 72 to determine approximately what rate of return is needed for an investment to double in value every 8 years. (b) Use the Excel formula to check your approximate answer in Part (a).

6. Assume that you recently obtained a 30-year, 12% APR fixed-rate, $220,000 mortgage, which requires equal monthly payments (at end of each month) of $2,365.81. (a) If interest is compounded monthly, how much of the first payment goes towards reducing the loan balance? (b) How much total interest will you pay on the loan?

7. Suppose your daughter is 8 years old today. She plans to go to WWU when she turns 18 and take accounting (Toews will be retired by then!). You are worried about paying for her college tuition, which you estimate will be $21,000 per year (after scholarships). You decide to start a college savings fund by depositing an equal amount in the bank at the end of each of the next 10 years. At the end of years 11, 12, 13 and 14, you want to withdraw $21,000 in order to pay for the tuition. An interest rate of 8% APR compounded annually is assumed. How much do you have to deposit at the end of each of the next 10 years in order to pay for the tuition costs?

8. Archibald Andrews has just learned that he won $1,040,000 in the lottery. Archie has three options for payment: Option A: a lump-sum payment of $1,040,000 right now, in which case 45% will be deducted for taxes. We do not know the level of Archie’s investment skills and therefore are unsure what rate of return he will earn on the lumpsum. Option B: 20 equal annual payments of $72,000, the first to occur immediately. Taxes of 25% of will be deducted from each payment. Assume an inherent interest rate of 8% APR. Option C: 36 equal semi-annual payments of $36,000, the first to occur in exactly one year. Taxes of 15% will be deducted from each payment. For this option, assume interest of 8% APR, compounded semi-annually. Calculate the present value of each option a, b, and c.