Warm - Up A = d(1+r a )[(1+r a ) nt – 1] r a If you deposit $50 every quarter in an account that pays 5% interest compounded quarterly what will your balance be in 10 years? d = 50 r a = 0.05/4 = nt = 4*10 = 40 A = 50(1.0125)[(1.0125) 40 – 1] = $2,

A = d(1+r a )[(1+r a ) nt – 1] r a You deposit $1,000 every month in an account that pays 2.4% interest compounded monthly and leave it in the account for 4 years. 1)Show the above equation with all the correct values plugged in. 2)Solve your expression and list the account balance after 4 years. When you finish: fold your quiz in half and hold it in the air for Mr. F to collect. d = 1,000 r a = 0.024/12 = nt = 12*4 = 48 A = 1000(1.002)[(1.002) 48 – 1] = $50,

Turn to page 441!

7.5 – A Balancing Act Open up to page 441 and complete problems # 1 – 2. Interest = Balance at year end – Beginning balance Balance at year end = (1+.05/12)^12 for year 1 Thus for year 1 Interest Earned is and ending balance is Complete the table

7.5 – A Balancing Act For #1 part d you will need your calculator and the “Using your calculator to solve a recursive relationship” handout You will also need your calculator for #2 part a. to perform that recursive relationship.

7.5 – A Balancing Act Continue on page 442 and complete problem # 3. A = P(1 + r/n) nt – Withdrawal Complete the interest column this time! Once you notice the pattern you can stop with the calculations!!!

7.5 – A Balancing Act Equilibrium: –When you withdraw the same amount from your account that your interest accumulates each year. –This way your account balance at the end of the year is constant or the same.

7.5 – A Balancing Act Equilibrium Example: –Suppose you deposit $10,000 in a bank account that pays 5% interest annually. At the end of each year your Withdraw 500. What will your ending balance be after one year? A = $10,000(1.05) – $500 = $10,000 Interest = Withdrawal $10,000*.05 = $500

7.5 – A Balancing Act Continue on page 444 and complete problems # –Amount Devalued = Previous worth * 0.02 –Amount Deposited is always $300 –Current Worth = Previous – Devalue + Deposit –∆W = Current Worth – Previous Worth

So many equations, so little time! How do you know when to use the correct equation for savings account problems? Compound Interest: A = P(1 + r/n) nt Continuous Compounding: A = Pe rt Constant Deposits: A = d(1+r a )[(1+r a ) nt – 1] r a So many equations, so little time!

Savings Account Problems If you deposit $30 every quarter in an account that pays 5% interest compounded quarterly what will your balance be in 6 years? $30 every quarter! It’s a constant deposit account! A = d(1+r a )[(1+r a ) nt – 1] r a

Savings Account Problems If you deposit $540 in an account that pays 9.1% interest compounded continuously what will your balance be in 20 years? Compounded continuously!!! A = Pe rt

Savings Account Problems If you deposit $1,000 in an account that pays 12.3% interest compounded monthly. what will your balance be in 8 years? One deposit compounded monthly! A = P(1 + r/n) nt

Equilibrium Worksheet!! Ending Balance = P(1 + r) – Withdrawal Beginning Balance = Ending Balance from last year Interest = Beginning Balance * rate