Question

1. Prove: A constant rate of simple interest results in an effective rate of interest that is decreasing with respect to time.

2. An accumulation function is of the form a(t) = xt3 + yt2 + z, x, y, z ∈ IR. Katrina invested $5000 in an account that is subject to this accumulation function. At the end of 10 years, she has $31,000 in the account. Mackenzie, on the other hand, deposited $3,000 in the same account but left her money untouched for 17 years. At the end of 17 years, she has $72,360. (a) Cameron wants to have $100,000 at the end of 13 years and wants to invest in an account that is subject to this accumulation function. How much should she invest now? (b) Determine Cameron’s annual effective rate of interest for the ninth year.

3. On February 14, Gian borrows $15,000 from Michael. Gian gave Michael a promissory note agreeing to repay his debt on August 30 at a 3.5% annual rate of simple interest. On April 17, Michael sells the promissory note to Paulo for $C. The annual rate of simple interest that Paulo paid is 4%. Determine the value of C and the annual rate of simple interest that Michael earned while holding the note.

4. Matthew wants to have $50,000 in fifteen years. The best option that he has is to invest in a fund that earns 1.5% annual effective interest rate for the first three years, 3.75% nominal annual rate compounded quarterly for the next four years, and 5.5% annual effective rate of discount thereafter. (a) How much should Matthew invest now so he will realize his goal at the end of 15 years? (b) Determine Matthew’s average annual compound interest rate over the 15-year period.

5. Patricia borrows $30,000 at an annual effective rate of 4%. She agrees to repay the loan by making a payment of $20,000 at the end of T years and a payment of $25,600 at the end of 2T years. Determine T.

6. Bianca opened an account and deposited $5000 on July 1, 2009, $3500 on July 1, 2011, and $3000 on July 1, 2016. On July 1, 2015 and July 1, 2018, she withdrew $2000 and $1000, respectively. The account earned at a nominal annual interest rate of 9% compounded monthly for the first three years, an effective annual discount rate of 7% for the next two years,and a nominal annual rate of discount compounded semiannually of 8% thereafter. Determine the balance in her account on July 1, 2019.

Answer 1