Rebecca caluclated that she needs a total of $1,400,000 at retirement (beyond pe
ID: 2753167 • Letter: R
Question
Rebecca caluclated that she needs a total of $1,400,000 at retirement (beyond pensions and social security). Rebecca is 34 years old, investing aggressively and expecting to earn 7% in her retirment account. She plans to retire at age 62.
How much does she need to save annually to achieve her goal?
once in retirment, rebecca would like annual retirment income of 70,000. She would like the savings to last for 25 years during retirment. Assuming that she could earn a 4% after tax and after inflation rate of return on their investments, did she save enough?
Explanation / Answer
Future value of annuity = P×[(1+r)^n-1]÷r
r is interest rate per period
P is payment per period
n is number of payments
$1,400,000 = P×[(1+7%)^28-1]÷7%
Annul saving required, P = $17,348.70
Present value of annuity = P×[1-(1÷(1+r)^n)]÷r
r is interest rate per period
P is payment per period
n is number of payments
= $70,000×[1-(1÷(1+4%)^25)]÷4%
= $1,093,545.60
She saved enough. She withdrawing less than what she can for 25 years.
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