A patty stacey deposits 1200 at the end of each of 5 years...

(a) Patty Stacey deposits $1200 at the end of each of 5 years in an IRA. If she leaves the money that has accumulated in the IRA account for 25 additional years, how much is in her account at the end of the 30-year period? Assume an interest rate of 11%, compounded annually. (Round your answer to the nearest cent.) $ (b) Suppose that Patty's husband delays starting an IRA for the first 10 years he works but then makes $1200 deposits at the end of each of the next 15 years. If the interest rate is 11%, compounded annually, and if he leaves the money in his account for 5 additional years, how much will be in his account at the end of the 30-year period? (Round your answer to the nearest cent.) $ (c) Does Patty or her husband have more IRA money?

Transcript

00:01 So here the solution for this problem is as for the first condition here we have the principle as $1 ,200 and we have n as equals to pi and we have i as equals to 11%.

00:15 So here the formula will be a equals to p multiplied with 1 plus i whole power n minus 1.

00:25 So here by using this formula we will calculate the total amount for the deposit of each year so for the first year it will be p multiplied with 1 plus i whole power n minus 1 so this will come as 1200 multiplied with 1 plus i is 11 % so we can write the 11 % as 0 .111 whole power 5 minus 1 so this will be equal to 1200 multiplied with 1 plus 0 .11 whole power 4 and for the second year second year it will be 1200 multiplied with 1 plus 0 .11 whole power 4 minus 1 which will be equals to 1200 multiplied with 1 plus 0 .11 whole power 3.

01:27 And for third year, it will be 1200 multiplied with 1 plus 0 .11 whole power 3 minus 1, which will be equal to 1200 multiplied with 1 plus 0 .11 whole square.

01:46 And for 4th year, it will be 1200 multiplied with 1 plus 0 .11 whole power 2 minus 1 so this will be equals to 1200 multiplied with 1 plus 0 .11 whole power 1 and for the fifth year it will be 12 hundred multiplied with 1 plus 0 .11 whole power 1 minus 1 so this will be 1.

02:22 Be equals to 1200 multiplied with 1 plus 0 .11 whole power 0 so the total amount will be total amount will be a equals to 1200 multiplied with so here we will take the 1200 as the common factor so this will give us the equation as 1200 multiplied with 1 plus 0 .11 whole power 4 plus 1 plus 1 1 plus 0 .11 whole power 3 plus 1 plus 0 .11 whole square plus 1 plus 0 .11 whole power 1 plus 1.

03:09 So by simplifying this we'll get the total amount as a equals to 7473 .36.

03:19 For extra 25 years, the total amount the total amount will be m equals to 7 ,473 .36 multiplied with 1 plus 0 .11 whole power 25.

03:37 So by simplifying this, we'll get the answer as 1 ,000 ,000 ,000 ,29 .06.

03:47 So this is the answer for the first condition...

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