Part 1: Single-payments

The formula that governs single amounts of money is
F =P(1+i)n (1)

where

F is “future value”
P is “present value”
i is the interest rate per period n is the number per periods

1-Suppose you have $100 today; how much will you have in 10
years, if your savings account pays 1% interest per annum? Note, 1%
is the same as i = 0.01.

2-Suppose you want to save for a $100 purchase 10 years in the
future. How much do you need to put in your bank account today, if
it pays 1% interest per year?

3-Suppose you have $100 today; how much did you have to deposit
in your savings account 10 years ago, if it pays 1% interest per
annum? (Hint: This should be a short/easy/repet- itive
question.)

Notice that the words “present” and “future” don’t actually mean
present and future, but that they indicate which values come first.
In this question, “today’s” value is F , and the value 10 years ago
is P .

Part 1.1: Interest compounding period not a year

In most real-life cases, interest rates are cited annually, but
compounded at periods less than a year. In this case, we need to
revise our interest rate i to match the equivalent compounding
period, and set our number of periods n to the equivalent number of
compounding periods.

4-Suppose we are considering a 5-year investment that is
compounded semi-annually (i.e. twice a year). What is the
appropriate n?

5-Suppose our investment pays 2% per annum, compounded
semi-annually. What is the appropriate i?

6-Compute the final value of our 5-year investment at 2% per
annum compounded semi- annually, if we invest $100 today.

7-Suppose 7 years ago, we borrowed $1200 in at 1% per annum,
compounded quarterly (i.e. 4 times a year). How much do we owe
today?

8-How much would we owe if our loan had compounded monthly? This
difference is the extra interest we have to pay.