Your client is 40 years old and she wants to begin saving for retirement, with the first payment to come one year from now. She can save 5000 per year; and you advise her to invest it in the stock market, Which you expect to provide and average 9% in the future.

A) If she follows your advice, how much money will she have at 65?

B) How much will she have at 70?

C) She expect to live for 20 years if she retires at 65 and for 15 years if she retires at 70. If her investments continue to earn the same rate, how much will she be able to withdraw at the end of each year after retirement at each retirement age?

Suppose that you save for retirement by contributing the same amount each month from your 23rd birthday until your 65th birthday, in an account that pays a steady 4% annual interest compounded monthly.

(a) How much will be in your fund at age 65 if you save $100 a month?

kijij

yes

PMT = $5000

i = 9%
N = 25
FVA25 = $5000 [( (1+〖9%)〗^25-1 )/(9%)]
= $423 504.4811
= $423 504.50

To calculate the future value of an investment, you can use the formula for the future value of an ordinary annuity. The formula is:

FV = P * [(1 + r) ^ n - 1] / r

Where:
FV = Future Value
P = Annual payment
r = Interest rate per period (in decimal form)
n = Number of periods

For part (A): If your client follows your advice and saves $5,000 per year for 25 years (from age 40 to age 65) with an average return of 9%, we can calculate the future value:

P = $5,000
r = 9% (0.09)
n = 25

FV = $5,000 * [(1 + 0.09) ^ 25 - 1] / 0.09
FV = $5,000 * (1.09 ^ 25 - 1) / 0.09
FV ≈ $267,372.67

Therefore, she will have approximately $267,372.67 when she reaches age 65.

For part (B): If she continues saving until age 70, we need to calculate the future value from age 40 to 70:

P = $5,000
r = 9% (0.09)
n = 30

FV = $5,000 * [(1 + 0.09) ^ 30 - 1] / 0.09
FV = $5,000 * (1.09 ^ 30 - 1) / 0.09
FV ≈ $728,040.50

Therefore, she will have approximately $728,040.50 when she reaches age 70.

For part (C): To determine how much she can withdraw each year after retirement, we can use the future value as the principal and calculate the annuity payment using the future value of an ordinary annuity formula:

PV = P * [(1 - (1 + r) ^ -n) / r]

Where:
PV = Present Value (future value of retirement savings)
P = Annual payment during retirement
r = Interest rate per period (in decimal form)
n = Number of periods (number of years in retirement)

For retirement at age 65:

PV = $267,372.67
r = 9% (0.09)
n = 20

PV = P * [(1 - (1 + 0.09) ^ -20) / 0.09]
$267,372.67 = P * [(1 - 1.09 ^ -20) / 0.09]
P ≈ $18,277.18

Therefore, she can withdraw approximately $18,277.18 per year for 20 years if she retires at age 65.

For retirement at age 70:

PV = $728,040.50
r = 9% (0.09)
n = 15

PV = P * [(1 - (1 + 0.09) ^ -15) / 0.09]
$728,040.50 = P * [(1 - 1.09 ^ -15) / 0.09]
P ≈ $81,340.70

Therefore, she can withdraw approximately $81,340.70 per year for 15 years if she retires at age 70.