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Financial Economics - Compounding and Present Value

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1. Compounding: Suppose someone invested 2 dollars on January 1, 1776 at 3.3 percent interest compounded yearly.
a) How much interest would the investment be worth on January 1, 2001 (225 years later)?
b) Suppose the interest rate were 6.6 percent instead of 3.3 percent. What would the investment be worth?
c) Suppose the interest rate was 6.6 percent in even years and 3.3 percent in odd years. How much would the investment be worth?

2. Present value: Suppose you are considering two job offers from investment banks. Their offers are different in that:
a) investment bank 1 promises to pay you 60,000 dollars per year and a signing bonus.
b) investment bank 2 promises to pay you 65,000 dollars per year but no signing bonus.
What is the minimum signing bonus you would ask of investment bank I to accept their offer? In calculating it, assume that:
- All dollar amounts above are certain and are adjusted for inflation.
- The real rate of interest is 3 percent.
- You plan to work for either bank for exactly 5 years before going to business school.
- You get the signing bonus today and you get your annual salary at the end of each year.

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Solution Preview

1. PV = 2 and interest rate = 3.3%
a) Number of years = 225
Compute FV = PV * (1+r)^n= 2 * (1+3.3%)^225 = $2975.79

b) When r = 6.6%, we compute
FV = PV * (1+r)^n= 2 * (1+6.6%)^225 = $ 3,518,852.40

c) We could combine the interest of two adjacent years
For every two years, the interest is ...

Solution Summary

In just under 230 words, this solution demonstrates how to solve for compound and present value. All calculations are shown and this is done in a step-wise manner.

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Question 2

Yakima is retiring this year with his savings in an investment fund worth $750,000. The fund has an average annual return of 9.00% (EAR).

a How much can Yakima withdraw at the end of each month (12 months per year) to have the fund last 30 years and still have $100,000 in the fund at the end of the 30 years (just to be safe)?

b How much can Yakima withdraw up front to invest in his home and still be able to withdraw $5,000 monthly for 30 years, with a zero balance at the end?

Initial Investment $750,000
EAR 9%
APR

Month Interest Withdraw Balance
0 0 0 $750,000
1 $67,500
2
3
4
5
6
7
8
9
10
11
12

Question 3 Score 0

The Smothers are looking at retiring and would like to be debt free when this starts. They presently owe $225,000 on their home mortgage that has a rate of 4.25% APR with monthly compounding.

a If they make payments of $3,000 monthly, how many years until they can retire (when the house loan is paid off).

b If in the upcoming 5 years, they make $2,000 monthly payments, and then sell their house for $500,000, how much will they have to buy a home in a retirement development? (All taxes and fees should be ignored)

A
Payments 3000
Rate 4.25%
Period 12
Time
PV $35,184.77

Monthly Rate 0.3542%

B
Presently Owe $225,000
Rate 0.3542%
Payments $2,000
Period 60
Amount Paid $120,000
$0.00

Question 4

Save-Your-Day loans advertises no-interest loans of $100 on which only a $1 fee per week is charged. Collateral is usually a car title. The borrower will not pay anything until the loan is paid off. Then the amount to be paid back is $1.00 for each week per $100 of loan value. For a loan of $200 (two loans of $100) for 3 weeks, the pay back amount would be $200 + $1.00 * 2 loans * 3 weeks = $200 + $6= only $206.
Louie borrows $500 and pays it back in 4 weeks. What effective annual rate will Save-Your-Day earn on the loan to Louie?

Question 5

Joan Dale inherited $500,000 that she invested at 12% APR compounded monthly and will not make any further payments. In 15 years when she retires, she will reinvest it in a more conservative fund that earns 5% APR with monthly compounding.

If she wants the retirement funds to last 25 years, how much will she receive monthly in her retirement years.

Question 6

Veronica borrowed $5,000 from her Uncle and the agreed upon interest rate is 4% annually (EAR)?

a What would be the result at the end of five years If she pays her uncle $100 a month?

b If each month she pays the interest (only) on the loan, how much would this be?

Question 7
Your client is considering two investments and has asked you to evaluate these alternatives. Provide financial and risk advice for your client regarding which to purchase.

a 500 shares of a stock that can be purchased for $80 a share. Forecasts are that it can be sold in 5 years for $135 a share. It also is forecasted to pay quarterly dividends of $2.00 per share in the upcoming 5 years.

b A bond with a face value of $50,000 that matures in 5 years. It can be purchased for $40,000 today, and it has a coupon rate of 5.00% that is paid semi-annually.

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