Math 141-copyright Joe Kahlig, 14B Page 1Section 5.2: AnnuitiesSection 5.3: Amortization and Sinking FundsDefinition: An annuity is an instrument that involves fixed payments be made/received at equaltime periods. An ordinary annuity is an annuity in which the payments are made at the end of eachperiod. A simple annuity is an annuity where the payments coincides with the interest conversionperiod. In this class we work with simple ordinary annuities.Formulas for simple ordinary annuities.account grows account declinesFuture Value Sinking Fund Present Value AmortizationF V = P M T[(1 + i)n− 1]iP M T =F V ∗ i[(1 + i)n− 1]P V = P M T[1 − (1 + i)−n]iP M T =P V ∗ i[1 − (1 + i)−n]1. Bob wants to deposit $100 at the end of every six months into an IRA that pays 7% compoundedsemiannually.A) How much money is in the account at the end of 25 years?B) How much money did Bob deposit into the account?C) How much interest did Bob get on the account?2. Sue is starting her bank account with $1000 and will deposit $100 each month for the next 6years. If the account pays 5.25% interest compounded monthly,A) How much will she have in the account at the end of 6 years?B) How much interest did she earn?C) How much interest was earned in the third year?Math 141-copyright Joe Kahlig, 14B Page 23. You have decided to set up a college fund for your kid. You have decided that $75,000 shouldbe enough to get Jr most of the way through college. You decide to open the account when Jris born and make monthly deposits every month for 18 years. The account pays interest at arate of 4.6% compounded monthly.A) What is your monthly deposit that would reach your goal?B) What is the ballance of the account after 10 years?C) How much money did you deposit into the account?D) How much interest did the account earn?4. You have decided that you want a new Chevy Truck in 5 years. It will cost $30,000. You aregoing to save up for the truck by making monthly payments into an account, paying 4.5% inter-est compounded monthly.A) What monthly payments should you make so that you can buy the truck with cash?B) What is the ballance of the account after 25 payments?Math 141-copyright Joe Kahlig, 14B Page 35. You have decided that you want a new Chevy Truck. However you want it right now. It willcost $30,000.A) What monthly payments should you make, paying 4.5% interest compounded monthly, sothat you can payoff the truck in 5 years?B) What payment would you have if there was a $9000 balloon payment at the end of the loan?6. After you retire, you would like to receive quarterly payments of $5,000 for the next 15 years.The account earns 8% compounded quarterly.A) What amount do you use to start the account?B) How much interest was earn during the lifetime of the account?Math 141-copyright Joe Kahlig, 14B Page 47. You just won $4 million in the lottery, but you choose the payment method instead of thecash option. This means that you will receive 20 payments of $200,000. How much should bedeposited into an account paying 9% compounded annually, so that you can receive the yourpayments for the next 19 years?8. You want to buy a house. The house will cost $120,000. You put 5% down and then plan to payoff the house for the next 30 years with monthly payments. What payments should you make topay off the loan if the interest rate is 7.5% compounded monthly? How much interest did youpay?9. repeat the house loan for a 15 year loan.10. Write an amortization schedule for the first 4 months for problem 8.amt. toward outstandingperiod interest owed payment principal principal0 — — —123411. How much equity would you have on the 30 year note after 5 years? after 10 years?Equity = value of the object - what you still oweMath 141-copyright Joe Kahlig, 14B Page 512. You had made payments on the 30 year mortgage for 7 years and then decide to refinance theloan for 15 years at 5.35%.A) What would be the new house payment?B) How much money would you save, not counting refinancing costs, by refinancing the loan?13. Your credit card has a balance of $2000 and the interest rate is 19.5% compounded monthly. Ifyou only make the minimum monthly payment of $35 per month, how many years will it taketo pay off the balance? How much interest did you pay? Assume that you are not making anymore charges on the card.14. You start an account with $1000 and then withdraw $40 at the end of every month. The accountearns interest at a rate of 6% per year compounded monthly.A) What is the ballance at the end of 1 year?B) How many full withdrawls of $40 are possible from this account?15. The local store has a flat screen tv for sale on a payment plan. The terms of the sale are thatyou make payments of $225 each month for 4 years at which time the tv will be paid off. Assumethat the rate for the account is 4.5% per year compounded monthly. What was the purchaseprice of the
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