Your retirement plan involves saving $25,000 per year at the end of each of the
ID: 2805832 • Letter: Y
Question
Your retirement plan involves saving $25,000 per year at the end of each of the next 20 years to produce savings that will be used to make equal annual retirement income payments to you of $50,000 at the end of each of the next 30 years. If the relevant interest rate is 5% per year, will you be in a deficit position (savings insufficient to fund pension payments) or a surplus position (savings greater than what is needed to fund pension payments) at the end of year 20?
Surplus of $68,322
Deficit of $47,554
Deficit of $107,304
Surplus of $58,026
None of the above
Explanation / Answer
answer is surplus of 58026.
the value of receipt of 50000 per year for 30 years at the end of 20 years from now= present value of annuity for 30 years at 5% for an amount of 50000 per year
and the value of annuity= 50000 * present value annuity factor for 30 years, 5%= 50000* 15.37= 768623
the future value of the contribution making every year from this year till the end of 20 years will be the future value of 25000 per year annuity for 20 years at 5%
future value= 25000* future value annuity factor at 20 years and 5%= 25000* 33.07= 826649
it looks like the amount of contributions made 826649 is more than the value of annuity present value 768623 by 58026 at the end of 20 years from now.
hence fourth option is correct
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