Question

(a) Patty Stacey deposits $2600 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 $2600 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?

Answer 1

Patty:

Amount deposited = $2600 every year for 5 years

Time for which money left untouched = 25 years after 5 years

Interest rate = 11%

So amount deposited at year 1 will be compounded for 30 years

So value of amount year 1 money deposited after 30 years = 2600 * (1.11)^30 = 59520

Similarly :

Value of amount year 2 money deposited after 30 years = 2600 * (1.11)^29 = 53621.6

Value of amount year 3 money deposited after 30 years = 2600 * (1.11)^28 = 48307.7

Value of amount year 4 money deposited after 30 years = 2600 * (1.11)^26 = 39207.6

Value of amount year 5 money deposited after 30 years = 2600 * (1.11)^25 = 35322.2

Total money after 30 years = sum of all of the above = 235979.10

Husband:

Amount deposited = $2600 started after 10 years and depositedevery year for 15 years

Time for which money left untouched = 5 years after 25 years

Interest rate = 11%

So amount deposited at year 10 will be compounded for 20 years

So value of amount year 10 money deposited after 30 years = 2600 * (1.11)^20 = 20962

Similarly :

Value of amount year 11 money deposited after 30 years = 2600 * (1.11)^19 = 18884.7

Value of amount year 12 money deposited after 30 years = 2600 * (1.11)^18 = 170132.2

Value of amount year 13 money deposited after 30 years = 2600 * (1.11)^17 = 15327.2

Value of amount year 14 money deposited after 30 years = 2600 * (1.11)^16 = 13808.3

Value of amount year 15 money deposited after 30 years = 2600 * (1.11)^15 = 12440

Value of amount year 16 money deposited after 30 years = 2600 * (1.11)^14 = 11207.1

Value of amount year 17 money deposited after 30 years = 2600 * (1.11)^13 = 10096.5

Value of amount year 18 money deposited after 30 years = 2600 * (1.11)^12 = 9096

Value of amount year 19 money deposited after 30 years = 2600 * (1.11)^11 = 8194.6

Value of amount year 20 money deposited after 30 years = 2600 * (1.11)^10 = 7382.5

Value of amount year 21 money deposited after 30 years = 2600 * (1.11)^9 = 6650.9

Value of amount year 22 money deposited after 30 years = 2600 * (1.11)^8 = 5991.8

Value of amount year 23 money deposited after 30 years = 2600 * (1.11)^7 = 5398

Value of amount year 24 money deposited after 30 years = 2600 * (1.11)^6 = 4863.1

Value of amount year 25 money deposited after 30 years = 2600 * (1.11)^5 = 4381.2

Total money after 30 years = sum of all of the above = 171697.1

Yes Patty has more money than her husband