A 45 year old woman decides to place funds in a retirement plan. She can save...

A 45 year old woman decides to place funds in a retirement plan. She can save
1,550 per year and earn 6 percent on this savings. How much will she have
accumulated if she retires at age 65? If this were an annuity due, how much
extra money would she have?

Solutions

Expert Solution

We need to use the concept of Future Value of Annuity here:

where P = Periodic Payment = 1,550 per year

r = Rate of Interest per Period = 6% = 0.06

n = number of years/periods = 65-45 = 20 years

Future Value of Annuity = 1,550 x [ (1+0.06)²⁰ - 1 ) / 0.06]

Future Value of Annuity = 1,550 x [ (1.06)²⁰ - 1 ) / 0.06]

Future Value of Annuity = 1,550 x [ ( 3.207135 - 1 ) / 0.06]

Future Value of Annuity = 1,550 x [ 2.207135 / 0.06]

Future Value of Annuity = 1,550 x 36.78559

Future Value of Annuity = 57,017.666 = 57,017.67

She would have accumulated 57,017.67 if she retires at age 65.

If this were an annuity due

Future Value of Annuity Due = [1,550 x [ (1+0.06)²⁰ - 1 ) / 0.06] x (1 + 0.06)

Future Value of Annuity Due = 1,550 x [ (1.06)²⁰ - 1 ) / 0.06] x (1.06)

Future Value of Annuity Due = 1,550 x [ ( 3.207135 - 1 ) / 0.06] x (1.06)

Future Value of Annuity Due = 1,550 x [ 2.207135 / 0.06] x (1.06)

Future Value of Annuity Due = 1,550 x 36.78559 x (1.06)

Future Value of Annuity Due = 60,438.726 = 60,438.73

Extra money she would have = Future Value of Annuity Due - Future Value of Annuity

= 60,438.73 - 57,017.67 = 3,421.06

jeff jeffy answered 1 year ago

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