Question

social security. a person scheduled to receive a $2000 monthly social security benefit at a full retirement age of 66 can delay drawing benefits until age 70 and receive $2640 per month. at what age will the person who started taking benefits at age 70 have more in total benefits paid than if he or she had started taking benefits at age 66?

Answer 1

82 years and 7 months.

(They will have the same total at 82.5 years)

Explanation:

Define the variables:

• Let x be the number of months after the age of 70.
• Let y be the total pay.

Given that $2,000 monthly social security benefit is paid at a full retirement age of 66, the amount paid from the age of 66 until the age of 70 is:

`\implies \$2,000 * 12 * 4 = \$96,000`

Therefore, from the age of 70, the equation for the total pay of a person who retired at the age of 66 is:

• 
  `y = 2000x+96000`

And from the age of 70, the equation for the total pay of a person who retired at the age of 70 is:

• 
  `y=2640x`

To find the age at which the person who started taking benefits at age 70 will have more in total than if they had started taking benefits at age 66, set the equation for the person who started taking benefits at age 70 more than the equation for the person who started taking benefits at age 66 and solve for x:

`\implies 2640x > 2000x+96000`

`\implies 640x > 96000`

`\implies x > 150`

150 months equals 12.5 years.

70 years + 12.5 years = 82.5 years

Therefore, at the age of 82.5 years, the person who started taking benefits at the age of 70 will have the same in total benefits paid as the person who started taking benefits at the age of 65.

Therefore, the age at which the person who started taking benefits at the age of 70 will have more in total benefits paid than if they had started taking benefits at age 66 is after 82.5 years. So 82 years and 7 months.

Answer 2

At age 82.5 the person that started taking benefits at age 70 would have more in total benefits.

Explanation:

2000 x 12 = 24,000 This is how much you would make for one year.

If you took that for the years 66, 67, 68 ,69, the total would be

24000 x 4 = 96000

The equation for how much money you would make starting at age 70 would be

y = 2000x + 96000

The equation if you stated taking money at 70 would be

y = 2640x

If we set these equations equal to each other we found find at what month the incomes would be equal.

2000x + 96000 = 2640x Subtract 2000x from those sides

96000 = 640x Divide both sides by 640

x = 150

150 months after 70 the amounts would be equal. this would be 12.5 years.

70 + 12.5 = 82.5