Question

Ron is 25 years old and is retiring at the age of 65. When he retires, he will need a monthly income of $4,123 for 20 years. If Ron contributes 10% of his monthly income to a 401(k) paying 5.5% compounded monthly, will he reach his goal for retirement given that his monthly income is 3,142.23? If he does not make his goal then state by what amount he will need to supplement his income. Round all answers to the nearest cent.

Answer 1

The answer is c i took the test

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Answer 2

Ron will not make his monthly goal of $4,123 and will need $359.74 to supplement his monthly income when he retires.

Explanation:

Given monthly income of Ron is $3,142.23

Ron contributes 10% of his monthly income that is $ 314.223

Given : Ron is 25 years old and is retiring at the age of 65. so he has 40 years to contribute.

Total amount he contribute in 40 years paying 5.5% compounded monthly is given by

interest rate(r) =
`(0.055)/(12)`

time period = 40 years = 480 months

Principal amount = $ 314.223

Future value =
`P(((1+r)^n-1)/(r) )`

Substitute , we get,

`=3142.23\cdot(.10\left(\left(1+(.055)/(12)\right)^(12\cdot40)-1\right))/((0.055)/(12))`

Thus, future value is $547074.681009.

After retirement his monthly income when he has $547074.681009 amount.

`P=(A\cdot(i)/(12) )/(1-(1+(i)/(12))^(-n))`

Putting values , we get,

`P=(\left(547074.68\cdot(.055)/(12)\right))/(1-\left(1+(0.055)/(12)\right)^(-240))`

P = $3763.25

He will receive a monthly income of $3763.25.

But given he will need a monthly income of $4,123 for 20 years which is not met by Ron.

So,the amount he need to supplement his monthly income when he retires by (4123-3763.25)= $359.74

Ron will not make his monthly goal of $4,123 and will need $359.74 to supplement his monthly income when he retires.