Question

Use the following information to answer each question Allison wants to save for retirement. She is 20 and wants to retire in 40 years. She is considering two options and expects to earn an 8% annual return under each option.

Option 1: She is considering contributing $6,000 per year to an IRA for 10 years at which time she figures she will be tired of self-deprivation save no more. The invested funds, however, will continue to grow until she retires.

Option 2: Her other option is to spend all her money now and worry about retirement later. Under this plan she will contribute 6,000 per year to her IRA every year from the time she's 30 until she retires 30 years later, thinking surely the extra contributions under this plan will make her better off.

Question 2 (1 point) How much will Allison have for retirement under Option 2? $1,554,339.11 O $679,699.27 $874,639.85 $86,919.37 Question 3 (1 point) What is the point illustrated by the previous questions? Investing for more years is more important than saving early. You are better off not using IRAs. The time value of money has little impact on one's retirement savings. One should start saving for retirement early to take advantage of the time value of money.

Answer 1

Solution:

Let us calculate the Future value with respect to both the option

Option 1:

Deposited amount = $6,000 per year

T = 10 years

Interest rate = 8%

FV of annuity after 10 years = P * [(1+r)^T - 1] / r = 6000 * [1.08^10 - 1] / 0.08 = 6953.5499 / 0.08 = 86919.37479

Since She will retire at the age of 60 hence this FV of 8691.9374 will grow at 8% for 30 more years

Future value when she retires = 86919.37479 * 1.08^30 = 874,639.85

Option 2 )

She starts at the age of 30 till retirement hence invested period = 30 years

Deposited amount = $6,000 per year

T = 30 years

Interest rate = 8%

FV of annuity after 10 years = 6000 * [(1+r)^T - 1] / r = 6000 * [1.08^30- 1] / 0.08 = 54375.9413/ 0.08 = 679,699.27

Question 1 )

She will have 679,699.27 at the time of retirement according to option 2

Question 2 )

OPtion 1 has given higher future value though the invested period is less in option 1 hence correct option is

D) One should start saving for retirement early to take advantage of time value of money