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4.1 Compound Interest 1. Find the simple interest on a $500 investment made for 2 years at an interest rate of 8%/year. What is the accumulated amount? 2. A bank deposit paying simple interest at the rate of 5%/year crew to a sum of $31000 in 10 months. Find the principal. 3. Find the accumulated amount after 4 years if $5000 is invested at 6%/year compounded (a) semiannually. (b) quarterly. (c) monthly (d) daily. (e) continuously. 4. How much money should be deposited in a bank paving interest at the rate of 6% per year so that at the end of 3 years, the accumulated amount will be $20,000.00 if the interest is compounded (a) annually? (b) quarterly? (c) continuously? 5. How long will it take $12,000 to grow to $15,000 if the investment earns interest at the rate of 4%/year compounded continuously? 6. Find the effective interest rate corresponding to the nominal rate of 6%/year compounded (a) semiannually. (b) quarterly. (c) monthly. (d) daily. 4.2 Annuities 7. Find the amount of an ordinary annuity consisting of 36 monthly payments of $250 each and earning interest at 5.5% per year compounded (a) semiannually. (b) quarterly. (c) monthly 8. Find the present value of an ordinary annuity consisting of 30 monthly payments of $1,500.00 each and earning interest at 4% per year compounded (a) serniannually. (b) quarterly. (c) monthly. 9. To save for the down payment of a house, the Johnsons decide to deposit $350 at the end of every month into a bank account paying interest at the rate of 7.5% per year compounded monthly. If they started saving in June 2005, how much do they have in the account at the start of December 20197 10. Lup made a down payment of $8000 toward the purchase of a new car. To pay the balance of the purchase price, she has secured a loan from her bank at the rate of 6%/year compounded monthly. Under the terms of her finance agreement, she is required to make payments of $420/month for 36 months. What is the cash price of the car? What portion of Lup's total car payments went toward interest? 4.3 Amortization and Sinking Funds 11. Suppose payments will be made for 9.25 years at the end of each month into an ordinary annuity earning interest at the rate of 3.25%/year compounded monthly. If the present value of the annuity is $42,000, what should be the size of each payment? 12. The price of a new car is $20,000. Assume that an individual makes a down payment of 25% toward the purchase of the car and secures financing for the balance at the rate of 6%/year compounded monthly. (a) What monthly payment will she be required to make if the car is financed over a period of 36 months? Over a period of 48 months? (b) What will the interest charges be if she elects the 36-month plan? The 48-month plan? 13. Sarah purchased a house 8 years ago for $240,000.00. She made a down payment of 15% of the purchase price and secured a 30-year conventional home mortgage at 5% per year compounded monthly on the unpaid balance. (a) What is the outstanding principal on Kim's house now? (b) If the house is now worth $295,000.00, how much equity does Kim have on her house now? 14. Robin wishes to accumulate $450,000.00 in a retirement account by the time of her retirement 30 years from now. If she wishes to do this through monthly payments into an account earning interest at the rate of 6%/year compounded monthly, what should be the size of each payment? 15. Jennifer is the owner of a video game and entertainment software retail store. She is currently planning to retire in 30 years and wishes to withdraw $10,000.00/month for 20 years from her retirement starting at that time. How much must she contribute each month for 30 years into a retirement account earning interest at the rate of 48/year compounded monthly to meet her retirement goal
