Aim: Money Matters – Future Value of Annuities Course: Math Literacy Aim: How does money matter? Annuities – a savings plan for the future. Do Now: At the end of every month for the next six months you deposit $60 in an account that earns 12% compounded monthly. How much would you have at the end of the 6 th month? today 1 st m. 2 nd 3 rd 4 th 5 th 6 th 0 60( ) 5 = ( ) 4 = ( ) 3 = ( ) 2 = ( ) 1 = Total

Aim: Money Matters – Future Value of Annuities Course: Math Literacy A Savings Plan – An Annuity What size deposit do you need to make regularly in an account with a fixed interest rate, to have a specific amount at a particular time in the future? Ex. A graduate at her first job saves $100 per month, deposited directly into her credit union account on payday, the last day of the month. The account earns 1.8% per year compounded monthly. How much will she have at the end of five years? Annuity – a sequence of payments into or out of an interest-bearing account; a specified number of periodic payments

Aim: Money Matters – Future Value of Annuities Course: Math Literacy A Savings Plan Ex. A graduate at her first job saves $100 per month, deposited directly into her credit union account on payday, the last day of the month. The account earns 1.8% per year compounded monthly. How much will she have at the end of five years? interest rate for compounded period A = 100( ) 0 last deposit earns = 100 A = 100( ) 1 next to last A = 100( ) 2 3 rd from last A = 100( ) 59 1 st deposit = = = Add up all 60 returns for total or Find the Sum of a Finite Geometric Sequence

Aim: Money Matters – Future Value of Annuities Course: Math Literacy Find the sum of the first eight terms of the geometric sequence 1, 3, 9, 27,... The Sum of a Finite Geometric Sequence The sum of the finite geometric sequence a 1, a 1 r 2, a 1 r 3, a 1 r 4,.... a 1 r n with common ratio r  1 is given by r = 3

Aim: Money Matters – Future Value of Annuities Course: Math Literacy A Savings Plan Ex. A graduate at her first job saves $100 per month, deposited directly into her credit union account on payday, the last day of the month. The account earns 1.8% per year compounded monthly. How much will she have at the end of five years? Note: r in S n is ratio not interest; r = n is the number of compounding: 60 i is interest rate for n th period n is number of deposits d is amount of period deposit

Aim: Money Matters – Future Value of Annuities Course: Math Literacy A Savings Plan – Traditional Formula Ex. A graduate at her first job saves $100 per month, deposited directly into her credit union account on payday, the last day of the month. The account earns 1.8% per year compounded monthly. How much will she have at the end of five years? Future value, A, of an annuity Future Value (A); m – periodic payment; r – annual rate; t – time in years; and n – number of times per year payment is made

Aim: Money Matters – Future Value of Annuities Course: Math Literacy Model Problem How much do you save in 5 years if you deposit $60 at the end of each month into and account paying 12% compounded monthly? r = 0.12 m = 60 t = 5 n = 12

Aim: Money Matters – Future Value of Annuities Course: Math Literacy Model Problem Financial advisors stress the importance of beginning early to save for retirement. Many offer a 401k plan which allows an employee to make monthly contribution to a retirement account. The plan has the advantage that income tax on the contributions is deferred until the employee withdraws the money during retirement. You start a 401k when you turn 23 and contribute $50 at the end of each month until you turn 65 and retire. You put your money in a safe investment fund that earns a steady 5% annual interest compounded monthly. How much will you retirement fund be worth at retirement?

Aim: Money Matters – Future Value of Annuities Course: Math Literacy Model Problem You start a 401k when you turn 23 and contribute $50 at the end of each month until you turn 65 and retire. You put your money in a safe investment fund that earns a steady 5% annual interest compounded monthly. How much will you retirement fund be worth at retirement? r = 0.10 m = 200 t = 5 n = 12