Assume you deposit $4,900 at the end of each year into an account paying 11.75 p

Question

Assume you deposit $4,900 at the end of each year into an account paying 11.75 percent interest.

How much money will you have in the account in 22 years? (Enter rounded answer as directed, but do not use rounded numbers in intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).)

How much will you have if you make deposits for 44 years? (Enter rounded answer as directed, but do not use rounded numbers in intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).)

Assume you deposit $4,900 at the end of each year into an account paying 11.75 percent interest.

Explanation / Answer

1. Amount of annuity = $4,900. n = 22 years r = 11.75%. As payments are done at the end of year it is an ordinary annuity.

So we have to calculate the future value of each payment. FV of the payment made at the end of each year = amount*(1+rate)^(22 years - t)

This formula has been used to calculate the amount:

Amount = $438,698.88

2. When n = 44 years:

Amount = $5,492,431.13

Year Amount Discount factor FV 1 4900 1.1175 50,511.96 2 4900 45,200.86 3 4900 40,448.20 4 4900 36,195.26 5 4900 32,389.49 6 4900 28,983.88 7 4900 25,936.36 8 4900 23,209.27 9 4900 20,768.92 10 4900 18,585.17 11 4900 16,631.02 12 4900 14,882.35 13 4900 13,317.54 14 4900 11,917.26 15 4900 10,664.21 16 4900 9,542.92 17 4900 8,539.53 18 4900 7,641.63 19 4900 6,838.15 20 4900 6,119.15 21 4900 5,475.75 22 4900 4,900.00 Total 438,698.88

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