Aim: Money Matters-Annuities & Sinking Funds Course: Math Literacy Aim: How does money matter? Annuities – a savings plan. Do Now: You are 21 years old and will make monthly deposits to a bank account that pays 10% annual interest compounded monthly. Option 1: Pay yourself $200 per month for 5 years and then leave the balance in the bank until 65. (Total deposits 200 x 5 x 12 = $12,000) Option 2: Wait until your are 40 years old and then deposit $200 per month until age 65. Total deposits 200 x 25 x 12 = $60,000) Compare the two options.

Aim: Money Matters-Annuities & Sinking Funds Course: Math Literacy Model Problem You are 21 years old and will make monthly deposits to a bank account that pays 10% annual interest compounded monthly. Option 1: Pay yourself $200 per month for 5 years and then leave the balance in the bank until 65. (Total deposits 200 x 5 x 12 = $12,000) Option 2: Wait until your are 40 years old and then deposit $200 per month until age 65. Total deposits 200 x 25 x 12 = $60,000) Compare the two options.

Aim: Money Matters-Annuities & Sinking Funds Course: Math Literacy Model Problem Option 1: Pay yourself $200 per month for 5 years and then leave the balance in the bank until 65. (Total deposits 200 x 5 x 12 = $12,000). r = 0.10 m = 200 t = 5 n = 12 Annuity value at end of 5 years. Future Value at 65 t = 65 – 26

Aim: Money Matters-Annuities & Sinking Funds Course: Math Literacy Model Problem Option 2: Wait until your are 40 years old and then deposit $200 per month until age 65. (Total deposits 200 x 25 x 12 = $60,000) r = 0.10 m = 200 t = 25 n = 12 Annuity value at age of 65

Aim: Money Matters-Annuities & Sinking Funds Course: Math Literacy Model Problem How would the results of the two options affect your retirement if you live on interest only and earn the interest rate of 10%? I = Prt I = 752,850.86(0.10)(1/12) I = $6, monthly income I = Prt I = 265,366.68(0.10)(1/12) I = $2, monthly income

Aim: Money Matters-Annuities & Sinking Funds Course: Math Literacy Sinking Funds – Geometric Sequence Your parents started saving for your college education when you were born. How much would they have to save each month to accumulate $15,000 over 18 years with an account earning a steady 5% per year compounded monthly? = Sinking Fund – savings plan to accumulate a fixed sum by a particular date through equal periodic deposits.

Aim: Money Matters-Annuities & Sinking Funds Course: Math Literacy Model Problem – Traditional Formula Your parents started saving for your college education when you were born. How much would they have to save each month to accumulate $15,000 over 18 years with an account earning a steady 5% per year compounded monthly? Sinking Fund Formula Future Value (A); m – periodic payment; r – annual rate; t – time in years; and n – number of times per year payment is made r = 0.05 A = 15,000 t = 18 n = 12

Aim: Money Matters-Annuities & Sinking Funds Course: Math Literacy Model Problem You wish to have $10,000 in 5 years and decide to make monthly payment into an account paying 8% compounded monthly. What is the amount of each monthly payment? Future Value (A); m – periodic payment; r – annual rate; t – time in years; and n – number of times per year payment is made r = 0.08 A = 10,000 t = 5 n = 12 monthly payment of $136.10