Question

In: Finance

You want to be able to withdraw $35,000 from your account each year for 15 years...

You want to be able to withdraw $35,000 from your account each year for 15 years after you retire. If you expect to retire in 30 years and your account earns 7.8% interest while saving for retirement and 6% interest while retired: Round your answers to the nearest cent as needed. a) How much will you need to have when you retire? $ b) How much will you need to deposit each month until retirement to achieve your retirement goals? $ c) How much did you deposit into you retirement account? $ d) How much did you receive in payments during retirement? $ e) How much of the money you received was interest? $

Expert Solution

a]

PV of annuity = P * [1 - (1 + r)-n] / r,

where P = periodic payment. This is $35,000

r = interest rate per period. This is 6%

n = number of periods. This is 15.

PV of annuity = $35,000 * [1 - (1 + 6%)-15] / 6%

PV of annuity = $339,928.71

b]

Future value of annuity = P * [(1 + r)n - 1] / r,

where P = periodic payment. We need to calculate this.

r = periodic rate of interest. This is 7.8%

n = number of periods. This is 30

$339,928.71 = P * [(1 + 7.8%)30 - 1] / 7.8%

P = $339,928.71 * 7.8% / [(1 + 7.8%)30 - 1]

P = $3,112.62

c]

Amount deposited into retirement account = monthly deposit * total number of deposits

Amount deposited into retirement account = $3,112.62 * 30

Amount deposited into retirement account = $93,378.51

d]

Amount received in payments = monthly payment * total number of payments

Amount received in payments = $35,000 * 15 = $525,000

e]

Interest = Amount received in payments - Amount deposited into retirement account

Interest = $525,000 - $93,378.51

Interest = $431,621.49

jeff jeffy answered 2 years ago

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