Financial Math

Homework 2

September 13, 2022

1. (Problem 3.3) Assume that A(t) = 100 + 5t.

(a) Find i5.

(b) Find i10.

2. (Problem 3.9) John wants to have $800. He may obtain it by promising to pay $900 at the end of one year; or he may borrow $1,000 and repay $1,120 at the end of the year. If he can invest any balance over $800 at 10% for the year, which should he choose?

3. (Problem 4.5) What simple interest rate is necessary for $10,000 to earn $100 interest in 15 months?

4. (Problem 4.22) If A(4) = $1,200 and A(n) = $1,800,

(a) what is A(0), assuming a simple interest of 6%?

(b) what is n if i = 0.06 assuming simple interest?

5. (Problem 6.2) Jack has deposited $1,000 into a savings account. He wants to withdraw it when it has grown to $2,000. If the interest rate is 4% annual interest compounded annually, how long will he have to wait?

6. (Problem 6.10) Bruce and Robbie each open up new bank accounts at time 0. Bruce deposits 100 into his bank account, and Robbie deposits 50 into his. Each account earns the same annual effective interest rate. The amount of interest earned in Bruce’s account during the 11th year is equal to X. The amount of interest earned in Robbie’s account during the 17th year is also equal to X. Calculate X.

7. (Problem 7.4) It is known that an investment of $500 will increase to $4,000 at the end of 30 years. Find the sum of the present values of three payments of $10,000 each which will occur at the endof 20, 40, and 60 years.

8. (Problem 7.7) Sally has two IRA’s. IRA #1 earns interest at 8% effective annually and IRA #2 earns interest at 10% effective annually. She has not made any contributions since January 1, 1985, when the amount in IRA #1 was twice the amount in IRA #2. The sum of the two accounts on January 1, 1993 was $75,000. Determine how much was in IRA #2 on January 1, 1985.

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