1. (Monthly compounding) If you bought a $1,000 face value CD that matured in nine months, and which was advertised as paying 9% annual interest, compounded monthly, how much would you receive when you cashed in your CD at maturity?
2. (Annualizing a monthly rate) You credit card statement says that you will be charged 1.05% interest a month on unpaid balances. What is the Effective Annual Rate (EAR) being charged?
3. (FV of annuity due) To finance your newborn daughter's education you deposit $1,200 a year at the beginning of each of the next 18 years in an account paying 8% annual interest. How much will be in the account at the end of the 18th year?
4. (Rate of return of an annuity) Paul's Perfect Peugeot says they'll sell you a brand new Italian"Iron Man" motor scooter for $1,699. Financing is available, and the terms are 10% down and payments of $46.57 a month for 40 months. What annual interest rate is Paul charging you?
5. (Rate of return of an annuity) You would like to have $1,000,000 40 years from now, but the most you can afford to invest each year is $1,200. What annual rate of return will you have to earn to reach your goal?
6. (Monthly loan payment) Best Buy has a flat-screen HDTV on sale for $1,995. If you could borrow that amount from Carl's Credit Union at 12% for 1 year, what would be your monthly loan payments?
7. (Solving for an annuity payment) You would like to have $1,000,000 accumulated by the time you turn 65, which will be 40 years from now. How much would you have to put away each year to reach your goal, assuming you're starting from zero now and you earn 10% annual interest on your investment?
8. (PV of a perpetuity) If your required rate of return was 12% a year, how much would you pay today for $100 a month forever? (that is, the stream of $100 monthly payments goes on forever, continuing to be paid to your heirs after your death)
9. (PV of an uneven cash flow stream) what is the PV of the following project?
(Assume r = 10%)
Year Cash Flow
10. (FV of an uneven cash flow stream) what is the FV at the end of year 4 of the following project?
(Assume r = 10%)
Year Cash Flow
The solution solves various time value of money problems in the attached Excel file.
Compute the present value of this stream of income at a discount rate of 8%. Compare the present values of the income stream under the three discount rates.
Suppose you just inherited a gold mine. This gold mine is believed to have three years worth of gold deposit. Here is how much income this gold mine is projected to bring you each year for the next three years:
Year 1: $42,000,000
Year 2: $62,000,000
Year 3: $99,000,000
Compute the present value of this stream of income at a discount rate of 8%. Remember, you are calculating the present value for a whole stream of income, i.e. the total value of receiving all three payments (how much you would pay right now to receive these three payments in the future). Your answer should be one number - the present value for this oil well at a 8% discount rate but you have to show how you got to this number.
Now compute the present value of the income stream from the gold mine at a discount rate of 6%, and at a discount rate of 4%. Compare the present values of the income stream under the three discount rates.