1. (Problem 1.7) Compounding is the process of adding accumulated interest back to

the principal, so that interest is earned on interest from that moment on. In this case,

we have the formula A = P(1 + i)

t and we call i a yearly compound interest. You

can think of compound interest as a series of back-to-back simple interest contracts.

The interest earned in each period is added to the principal of the previous period to

become the principal for the next period. You borrow $10,000 for three years at 5%

annual interest compounded annually. What is the amount value at the end of three

years?

2. (Problem 1.9) Using the compound interest formula, what annual interest rate would

cause an investment of $5,000 to increase to $7,000 in 5 years?

3. (Problem 1.10) Using compound interest formula, how long would it take for an investment of $15,000 to increase to $45,000 if the annual compound interest rate is

2%?

4. (Problem 2.5) $100 is deposited at time t = 0 into an account whose accumulation

function is a(t) = 1 + 0.03√

t.

(a) Find the amount of interest generated at time 4, i.e., between t = 0 and t = 4.

(b) Find the amount of interest generated between time 1 and time 4.

5. (Problem 2.7) Suppose that a(t) = 0.10t

2 + 1. The only investment made is $300 at

time 1. Find the accumulated value of the investment at time 10.

6. (Problem 2.22) Suppose that a(t) = 0.1t

2 + 1. At time 0, $1,000 is invested. An

additional investment of $X is made at time 6. If the total accumulated value of these

two investments at time 8 is $18,000, find X.

7. Also, please answer the following two questions.

(a) Describe your career goals.

(b) Describe your interest in financial math and the course. What do you hope to get

out of it? What aspects of financial math most interest you?

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