## Question

You observe an investment that pays $500 a year for the next 10 years with the first cash flow occurring at the end of year 1. If you require a 7 percent rate of return, how much is this

investment worth to you today? Show your work!

Question 2 (3 marks)

You invest $500 a year for the next 10 years and the cash flows start at the end of year 1. If you require a 7 percent rate of return, how much is this investment worth to you at the end of 10 years? Show your work!

Question 3 (6 marks)

You observe an investment that pays annual cash flows. The cash flows will grow at 7 percent for the next 7 years and then grow at a modest rate of 2 percent per year forever. The first cash flow of $500 will occur at the end of year 1. If you require a 7 percent rate of return, how much is this investment worth to you today? Show your work!

Question 4 (4 marks)

Your great great grandmother deposited $15.00 into an account on October 15, 1915. Her estate will be settled on October 15, 2015 and the account will have an estimated value of $8,148.02.

What annual interest rate will the account have earned each year? Show your work!

Question 5 (2 marks each)

For each of the following examples, provide a description and the formula you would use to solve the problem.

A) A set of level cash flows occurring each time period for a fixed length of time.

B) A set of level cash flows occurring each time period forever.

C) A set of increasing cash flows occurring each time period for a fixed length of time.

D) A set of increasing cash flows occurring each time period forever.

E) A set of arbitrary cash flows occurring each time period for no more than 10 years.

Question 6 (A credit card myth, 5 marks)

A common myth about credit cards is that to build a good credit history you have to “carry a balance”, meaning you do not pay off the credit card balance every month, but only pay part of it. In addition to the fact that this myth is flat out wrong, it adds large amounts of interest to your credit card bill every month and makes it more expensive to pay off the total balance.

Suppose you currently have a credit card balance of $800 and you stop using the card for further purchases. The interest rate on your credit card is 1.7% per month (which is roughly 20% per year – a standard rate for a credit card) and the first payment is due in one month. How long does it take to pay off the balance on the card, if you only make the minimum required payment of $20 every month? (Take a guess before you calculate it!)

Question 7 (Deferred Student Loan, 10 marks)

Loans often have an option to “defer payments”. This means that for a certain time period the loan will still accumulate interest, but no payments have to be made. For example, suppose you take out a 15 year student loan with a 5-year deferment period, i.e., you won’t have to make any payments for the first five years of the loan contract, but starting at the end of year 6 you will make a total of 10 annual payments to pay off the loan. You estimate that you will be able to make payments of $4,000 each year. The interest rate of the loan is 9% p.a.

i) Calculate the present value of the loan payments at the end of year 5.

ii) Calculate the loan amount you will be able to take out (i.e., the present value of the loan payments at t=0).

iii) Now assume that the loan amount in ii) is not enough to cover your expenses while you are in college. You decide to increase the loan amount to $22,000. What will your 10 annual payments be? (Difficult!)

Question 8 (Alumni Donations, 6 marks)

When alumni donate to their alma mater, they often set up an endowment to ensure continuous long-term support. The structure of an endowment is such that the university cannot use the principal (i.e. the original amount of the donation) to cover costs, but it can use any investment income derived from the principal.

Assume a wealthy alumna just made a donation in form of an endowment to support the university library. She wants to guarantee that the library receives a $22,000 payment every year.

i) How large does the alumna’s endowment have to be, if the university can achieve a 5.5% rate of return on its investments and the first support payment will be paid in one year?

ii) Now assume the alumna wants to increase the size of the support payment every year by 1.8% to compensate the library for inflation. If the first support payment of 22,000 is made today, how large does the alumna’s donation have to be?

## Solution Preview

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Answer 1:Given that,

Time = 10 years

Rate = 7%

Annual payment = $500.

Present value of investment = [Annual payment * (1 – ((1 + Interest rate) ^ -Time))]/i

= (500 * (1 – (1 + 7%)-10)/7% = $3,511.80...