Question

An Individual Retirement Account (IRA) is an annuity that is set up to save for retirement. IRAs differ from TDAs in that an IRA allows the participant to contribute money whenever he or she wants, whereas a TDA requires the participant to have a specific amount deducted from each of his or her paychecks. When Shannon Pegnim was 14, she got an after-school job at a local pet shop. Her parents told her that if she put some of her earnings into an IRA, they would contribute an equal amount to her IRA. That year and every year thereafter, she deposited $500 into her IRA. When she became 25 years old, her parents stopped contributing, but Shannon increased her annual deposit to $1,000 and continued depositing that amount annually until she retired at age 65. Her IRA paid 7.5% interest. Find the following. (Round your answers to the nearest cent.) (a) The future value of the account $ (b) Shannon's and her parents' total contributions to the account Shannon $ Shannon's parents $ (c) The total interest $ (d) The future value of the account if Shannon waited until she was 19 before she started her IRA $ (e) The future value of the account if Shannon waited until she was 24 before she started her IRA

Answer 1

The future value of an annuity A over period N at interest rate of R is given by: A / R x [(1 + R)^N - 1]

Part (a)

A = $ 1,000 (Initially it was $ 500 each from Shannon and her parents, subsequently it was from her only; people making contribution changed, but the amount remained as same i.e. $ 1,000 per period)

R = 7.5%

N = 65 years - 14 years = 51 years

Hence, The future value of the account = A / R x [(1 + R)^N - 1] = 1,000 / 7.5% x [(1 + 7.5%)⁵¹ - 1] = $ 519,719.69 (Please round it off as per your requirement)

Part (b)

Shannon's contribution = $ 500 x (25 - 14) + $ 1,000 x (65 - 25) = $  45,500.00

Shannon's parents' contribution = $ 500 x (25 - 14) = $ 5,500

Part (c)

Interest = Total FV of the account - Shannon's contribution - Shannon's parents contribution = 519,719.69 - 45,500 - 5,500 = $  468,719.69

Part (d)

If Shannon had waited until 19

N = 65 - 19 = 46 years

Hence, The future value of the account = A / R x [(1 + R)^N - 1] = 1,000 / 7.5% x [(1 + 7.5%)⁴⁶ - 1] = $  357,969.35

Part (e)

If Shannon had waited until 24

N = 65 - 24 = 41 years

Hence, The future value of the account = A / R x [(1 + R)^N - 1] = 1,000 / 7.5% x [(1 + 7.5%)⁴¹ - 1] = $  245,300.76