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Your older brother turned 35 today, & he is planning to save
GH¢7,000/year for retirement, with the first deposit to be made
one year from today. He will invest in a mutual fund that's
expected to provide a return of 7.5%/year. He plans to retire 30
years from today, when he turns 65, & he expects to live for 25
years after retirement, to age 90. Under these assumptions, how
much can he spend each year after he retires? His first
withdrawal will be made at the end of his first retirement year

Respuesta :

Tundexi

The older brother will be able to spend an amount of GH¢64,932.21 each year for 25 years after retirement.

What is Formula for Future value of the annuity?

Future Value (FV) = P * ((1 + r)^n - 1/r)

FV = GH¢7,000 * (1+0.075)^{30} - 1/0.075]

FV = GH¢7,000 x (8.754955-1)/0.075

FV = GH¢7,000 x (7.754955/0.075)

FV = GH¢723,795.82

The amount of cash flow is derived and shows the current yearly savings will be available for him at the age of 65 and to be spent for the 25 years if he expects to live after retirement.

To determine the amount he is able to spend each year, we will copute that as follows:

  • PV = P x [1-(1+r)^{-n}/r] where PV= GH¢723,795.82, P= Expected periodic spending, R = 7.5%, n = 25 years

GH¢723,795.82 = P *  [1-(1+0.075)^{-25}/0.075]

GH¢723,795.82 = P * [(1-0.163979)/0.075]

GH¢723,795.82 = P * (0,836021 /0.075)

GH¢723,795.82 = P * 11.14695

P = GH¢723,795.82/11.14695

P = GH¢64,931.21

Therefore, the amount of GH¢64,932.21 will be spent each year for 25 years after retirement.

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