Topic Review — Loans, Investments and Annuities

← Loans, Investments and Annuities

This review covers compound interest, reducing balance loans, annuities, and comparing financial options.

Review Questions

1. $8 000 is invested at 5% p.a. compounded annually. What is the value after 4 years?
2. $15 000 is invested at 4.8% p.a. compounded monthly. Find the value after 3 years.
3. Write the recurrence relation for a $25 000 reducing balance loan at a monthly interest rate of 0.6% and monthly repayment of $800. Find the balance after month 1.
4. In month 1 of a $50 000 loan at 6% p.a. (0.5% monthly), a $400 repayment is made. How much of this payment goes to interest and how much reduces the principal?
5. Complete the repayment table for a $10 000 loan at 0.5% monthly, $350 repayments, for 3 months.
6. A loan balance is $3 500. Monthly interest rate is 0.8%, and the monthly repayment is $300. How many more months until the loan is paid off?
7. Write the recurrence relation for a future value annuity where $250 is deposited monthly at 0.4% monthly interest. Find the balance after 3 months.
8. Use the future value formula to find how much $400 monthly deposits at 5.4% p.a. (0.45% monthly) accumulate to after 18 months.
9. A retiree has $120 000 and withdraws $900 per month. The monthly interest rate is 0.4%. Write the recurrence relation and find the balance after 2 months.
10. A $60 000 annuity pays out $800 per month at 0.35% monthly interest. Approximately how many months will the fund last? (Use the PV formula.)
11. A $6 000 flat-rate loan charges 9% p.a. over 2 years. Find the total interest and monthly repayment.
12. A $6 000 reducing balance loan at 9% p.a. (0.75% monthly) has a monthly repayment of $272.48 over 24 months. Compare the total interest with the flat-rate loan in Question 11.
13. How much must be deposited monthly into an account earning 4.8% p.a. (0.4% monthly) to accumulate $20 000 in 36 months?
14. A borrower can afford $350 per month. They take out a $15 000 loan at 6% p.a. (0.5% monthly). Will they pay off the loan in 4 years (48 months)? Use the PV formula to check.
15. A home loan of $380 000 is offered at either 5.0% p.a. over 30 years or 5.4% p.a. over 25 years. Monthly repayments are $2 039.81 and $2 295.62 respectively. Compare the total interest paid and explain which you would recommend.