ASSIGNMENT 4 (TOTAL 30 MARKS)
1. You won [tex]$100 000 in a lottery and you want to set some of that sum aside for 10 years. After 10 years, you would like to receive $[/tex]2400 at the end of every 3 months for 8 years.
How much of your winnings must you set aside if interest is 5.5% compounded quarterly?
(3 marks)
2. A sum of money is deposited at the end of every month for 10 years at 7.5%
compounded monthly. After the last deposit, interest for the account is to be 6%
compounded quarterly and the account is to be paid out by quarterly payments of [tex]$4800 over six years. What is the size of the monthly deposit? (3 marks) 3. Compute the nominal annual rate of interest compounded semi-annually on a loan of $[/tex]48
000 repaid in installments of [tex]$4000 at the end of every 6 months in 10 years. (3 marks) 4. A loan of $[/tex]14 400 is to be repaid in end-of-the-quarter payments of [tex]$600. How many payments are required to repay the loan at 10.5% compounded quarterly? (3 marks) 5. The amount of $[/tex]574 is invested monthly at 6% compounded monthly for six years. The
balance in the fund is then converted into an annuity paying [tex]$3600 at the end of every three months. If interest on the annuity is 5.9% compounded quarterly, for how many months is the term of the annuity? (3 marks) 6. A loan was repaid over seven years by end-of-month payments of $[/tex]450. If interest was
12% compounded monthly, how much interest was paid? (3 marks)
7. Ms. Simms made deposits of [tex]$540 at the end of every three months into a savings account. For the first five years interest was 5% compounded quarterly. Since then the rate of interest has been 5.5% compounded quarterly. How much is the account balance after 13 years? (3 marks) 8. How much interest is included in the accumulated value of $[/tex]3200 paid at the end of
every six months for four years if the interest rate is 6.5% compounded semi-annually? (3
marks)
9. What is the size of deposits made at the end of each period that will accumulate to $67
200 after eight years at 6.5% compounded semi-annually? (3 marks)
10. Explain all types of annuities that you learned in this chapter (3 marks)
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