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. a. Ron will meet his monthly goal of exactly $4,123 for retirement. b. Ron will meet his monthly goal of $4,123 for retirement with an excess of $125.34. c. Ron will not make his monthly goal of $4,123 and will need $359.74 to supplement his monthly income when he retires. d. Ron will not make his monthly goal of $4,123 and will need $450.61 to supplement his monthly income when he retires.

Question

Mathematics

Jaida Stevenson

12 October, 04:17

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. a. Ron will meet his monthly goal of exactly $4,123 for retirement. b. Ron will meet his monthly goal of $4,123 for retirement with an excess of $125.34. c. Ron will not make his monthly goal of $4,123 and will need $359.74 to supplement his monthly income when he retires. d. Ron will not make his monthly goal of $4,123 and will need $450.61 to supplement his monthly income when he retires.

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Answers (2)

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Emery Pollard · Answer 1

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

Step-by-step explanation:

Ron is 25 years old and will retire at 65 years. This means Ron has (65 - 40) years = 40 years to contribute

Ron contributes 10% of his monthly laying 5.5% compounded monthly.

Monthly income = $3142.23

Ron's monthly contribution = 10% * 3142.23 = $314.223

Total amount contributed in 40 years after paying 5.5% compounded monthly interest is given as P ((1+r) ^n - 1) / r)

r = 5.5% = 5.5/100 = 0.055

For a month, r = 0.055/12 = 0.0045833333

Period (n) = 40*12 = 480 months

Initial / Principal amount = $314.223

Final amount = 314.223 ((1 + 0.0045833333) ^480 - 1) / 0.0045833333

= 314.223 ((1.0045833333) ^480 - 1) / 0.0045833333

= $547074.62

After retirement, Ron's monthly income is

P = (A * i/12) / 1 - (1 + i/12) ^-n

n = 20*12 = 240 months

P = (547074.68 * 0.055/12) / 1 - (1 + 0.055/12) ^-240

P = $3763.25

After retirement, Ron will receive $3763.26. But he will need a monthly income of $4123 for 20 years.

He needs to add (4123 - 3763.26) = $359.74 to his monthly income when he retires.

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

Sierra Stevenson · Answer 2

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