Question

1) The amount of money earned by an investment of principal P with an (annual) interest rate of r with
interest compute continuously is given by P ert where t is the investment in years. In the following, all
amounts are invested in accounts where interest is compounded continuously.

(a) (15 pts) Assume that Alice invests $50000 at an interest rate of 5%. Create a table
that lists her income for t = 1, 2, . . . 5

(b) (15 pts) Bob has $40000 to invest. He invests this in an account with an interest rate of 2.5% that
gives a bonus of $500 at the end of every year. Create a table that lists his income
for t = 1, 2, . . . 5.

(c) (20 pts) At the end of 5 years, who has more money, Alice or Bob? What about at the end of 10
years and 15 years?

Answer 1

a) Effective interest rate for Alice= e^5%-1=5.127%

Hence, at the end year 1,2,3 ,4 &5 his account balance will be like above.

b)

For Bob:

At the end of 1,2,3,4 and 5 year his account balance will be like above.

c) At the end of 10 year Alice has $82436.06 and BOB has $65104.72. Hence, Alice has higher amount of money.

At the end of year 15 year Alice has $10850 and BOB has $83596.12. Hence, Alice has higher amount of money.