USA Bank offers a variety of annuities for a variety of situations. Different cu
ID: 2760604 • Letter: U
Question
USA Bank offers a variety of annuities for a variety of situations. Different customers want different accounts. (In this activity, Round all dollar amounts to the nearest cent, and report time in years and months.) Meredith is saving for a condo. She is depositing $250 a month into an ordinary annuity which earns 3% interest compounded monthly. Justin is saving for his son's college education. He wants to have $100,000 saved up over 17 years. He can deposit into an ordinary annuity which earns 6.2% interest compounded annually. Max is saving for retirement. He started depositing $1000 a year when he turned 24, into an ordinary annuity earning 4.8% interest compounded annually, but he had to stop depositing money when he turned 40. Minnie is saving for retirement. She didn't start depositing money until she turned 35, but then also deposited $1000 a year into an ordinary annuity earning 4.8% interest compounded annually. Sachiko deposited $300 a month for a year into an ordinary annuity compounded monthly. She ended up with $4000. Mathematical Analysis Determine how much money Meredith will have in her account after 2 years, and after 5 years. Determine when (after how many months) Meredith will have $25,000 in her account. Determine how much Justin would have to deposit each year to have saved $100,000 over 17 years. Determine how much money Max has for retirement when he turns 65. (Remember that Max gets interest on his money even when he isn't making deposits.) Determine how much money Minnie will have for retirement when she turns 65. (Here, Minnie keeps making deposits until she turns 65.] Determine how many years Minnie would have to make deposits in order to have the same amount of money Max has when he turns 65. (Here, Minnie keeps making deposits indefinitely.) Estimate the interest rate on Sachiko's account.Explanation / Answer
1. Ordinary annuity:
Futue value = payment { (1 + interest) time - 1 } / interest
= 1000 ( 1 + 0.048)42 - 1 ) / 0.048
= 1000 [(1.048)42 - 1 ] / 0.048
= 1000 * (7.164 - 1) / 0.048
= 1000 * 6.164 / 0.048
=128416.67
Note:- Time period = 42 years ( from the age of 24 till 65 years of age)
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