Question

Jeanette expects to live 30 years after she retires. At the end of the first year of her retirement, she wants to withdraw $35,000 from her savings. Each year thereafter, she wants to increase her annual withdrawal by 3.5 percent. If she can earn 5.5 percent on her savings, how much does she need to have in retirement savings on the day she retires

Answer 1

Answer:

$764,458.87

Step-by-step explanation:

Let say she has  Rs P at retirement

Interest earned on first Year = P * 5.5 * 1 /100  = 0.055P

Amount With drawn = $35,000

Amount in saving after 1 Year = 1.055P -35000

Interest in 2nd Year = ( 1.055P -35000) * 5.5 /100

Amount with drawn = 35000 * (1.035)

and so on on for 30 years

Then by applying Payout annuity formual for 30 yaers We can solve & get

= $764,458.87

Answer 2

Answer:

She needs $19,736,818.18

Step-by-step explanation:

We have 30 years after retirement.

For the first year, she wants to withdraw $35000 after which, for the rest of the 29 years she wants to withdraw 3.5% more of the $35000.

So we want to calculate what she will have

For the withdrawals after the first year will be 3.5% more of $35000

35000 = 100%, what about (100 + 3.5) So we have (35000 × 103.5) ÷ 100 = 36,225

So this 36,225 is what she will be withdrawing every year, for the 29 years.

In total, in the withdrawals in the 29 years will be

36,225 × 29 = 1,050,525

To get the total withdrawals for the 30 years, we will need to add the 35,000 to the 1,050,525;

1,050,525 + 35,000 = 1,085,525

So this is her total withdrawal for the 30 years.

So we assume that 1,085,525 is what earns her 5.5%. Therefore, we need 100% of this, to know what she needs to have for her retirement savings.

1,085,525 = 5.5% , what about 100%?

(1,085,525 × 100) ÷ 5.5 = 19,736,818.18

She needs $19,736,818.18 for her total retirement savings.