# Virtual high school

## Interest and Annuities Assignment

1. \$100 is deposited at the beginning of every week for five years in an account that pays 14%/a, compounded weekly.

a) What type of annuity is this?
b) Find the present value of the annuity using the formula.
c) Find the present value of the annuity using a spreadsheet. In your answer include the formulas that you typed.
d)Find the present value of the annuity using the TVM solver on a graphing calculator or on a website. In your answer, include what values you typed for each parameter.

2. Vanna has just financed the purchase of a home for \$200 000. She agreed to repay the loan by making equal monthly blended payments of \$3000 each at 4%/a, compounded monthly.

a) Create an amortization table using a Microsoft Excel spreadsheet. In your answer include all the formulas used.
b) How long will it take to repay the loan?
c) How much will be the final payment?
d) Determine how much interest she will pay for her loan.
e) Use Microsoft Excel to graph the amortization of the loan (Hint: Graph outstanding principal vs. month)
f) How much sooner would the loan be paid if she made a 15% down payment?
g) How much would Vanna have saved if she had obtained a loan 3%/a, compounded monthly?
h) Write a concluding statement about the importance of interest rates and down payments when taking out loans.

3. A lottery offers two options for the prize.
Option A: \$1000 a week for life.
Option B: \$600 000 in one lump sum.
The current expected rate of return for large investment is 3%/a, compounded monthly.

a) Which option would the winner choose if s/he expects to live for another 50 years?
b) At what point in time is Option A better than Option B?
c) To answer (3b), did you assume that the winner would never spend any of that money? Write a brief reflection about which option you would choose, and why (pay attention to the math, but reflect upon how much money you would want to be spending as opposed to saving).

4. Mary would like to save \$10 000 at the end of 5 years for a future down payment on a car.

a) How much should she deposit at the end of each week in a savings account that pays 1.2%/a, compounded monthly, to meet her goal?
b) If you currently have a part-time job, consider your hourly wage. If you do not have a job, use the minimum hourly wage in your jurisdiction. How many hours each week would you have to work, just to make those payments? Write a brief reflection on the advantages and disadvantages to long-term saving for a purchase, compared to borrowing a large sum of money and paying it off over time. Note that interest rates for savings accounts are always lower than interest rates for borrowing!