23 May WHAT IS THE EFFECTIVE ANNUAL INTEREST RATE ON THE LOAN?
A client invests $500,000 in a bond fund projected to earn 7 percent annually. Estimate the value of her investment after 10 years.
2) A client has agreed to invest $100,000 one year from now in a business planning to expand, and she has decided to set aside the funds today in a bank account that pays 7 percent compounded quarterly. How much does she need to set aside?
3) A couple plans to set aside $20,000 per year in a portfolio projected to earn 7 percent a year. If they make their first savings contribution one year from now, how much will they have at the end of 20 years?
4) You are considering investing in two different instruments. The first instrument will pay nothing for three years, but then it will pay $20,000 per year for four years. The second instrument will pay $20,000 for three years and $30,000 in the fourth year. All payments are made at year-end. If your rate of return on these investments is 8 percent annually, what should you be willing to pay for each instrument today?
5) A client seeking liquidity sets aside $35,000 in a bank account today. The account pays 5 percent compounded monthly. Because the client is concerned about the fact that deposit insurance covers the account for only up to $100,000, calculate how many months it will take to reach that amount.
6) A bank pays a stated annual percentage rate of 8 percent. What is the effective annual rate using the following types of compounding? i) Quarterly ii) Monthly iii) Continuous
7) A client plans to send a child to college for four years starting 18 years from now. She estimates the tuition and boarding costs to be $20,000 per year, payable at the beginning of each year, by the time her child goes to college. If she starts next year and makes 17 payments into a savings account paying 5 percent annually, what annual payments must she make?
8) If you take out an $8,200 car loan that calls for 48 monthly payments of $250 each, what is the APR of the loan? What is the effective annual interest rate on the loan? (This problem requires Excel)
9) Similar to what we did in class, derive an explicit formula for the present value of a growing annuity. (Do not just write down the formula. Please show where it comes from).
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