Question

Bilbo Baggins wants to save money to meet three objectives. First, he would like to be able to retire 30 years from now with retirement income of $27,000 per month for 25 years, with the first payment received 30 years and 1 month from now. Second, he would like to purchase a cabin in Rivendell in 15 years at an estimated cost of $693,000. Third, after he passes on at the end of the 25 years of withdrawals, he would like to leave an inheritance of $700,000 to his nephew Frodo. He can afford to save $2,000 per month for the next 15 years.

  

Required:

If he can earn a 11 percent EAR before he retires and a 8 percent EAR after he retires, how much will he have to save each month in years 16 through 30?

Answer 1

Solution :-

EAR Before Retire = 11%

Monthly rate before Retire = ( 1 + 0.11 )^1/12 - 1 = 1.008736 - 1 = 0.8736%

EAR after Retirement = 8%

Monthly Rate after Retire = ( 1 + 0.08 )^1/12 - 1 = 1.006434 - 1 = 0.6434%

Years of income after Retirement = 25

Therefore total Monthly Payments after Retirement = 25 * 12 = 300

Now Present Value at Retirement of Amount received after Retirement = $27,000 * PVAF ( 0.6434% , 300 )

= $27,000 * 132.7294

= $3,583,693.07

Present Value at Retirement that left after 25 years of Retirement = $700,000 / ( 1 + 0.08 )²⁵

= $700,000 * 0.14602

= $102,212.53

Now total Amount Required at Retirement = $3,583,693.07 + $102,212.53 = $3,685,905.60

Now the Value of next 15 Year ( 180 monthly Deposits ) Saving = $2,000 * FVAF ( 0.8736% , 180 )

= $2,000 * 433.355

= $866,710.21

Now after 15 Years value of Car Purchased = $693,000

Therefore Amount Left in Saving Account = $173,710.21

Now Assume the Value of monthly Saving from Year 16 to 30 be X ( 15 Years from now or 180 months )

= X * FVAF ( 0.8736% , 180 ) + $173,710.21 * ( 1 + 0.11 )¹⁵ = $3,685,905.60

( X * 433.355 ) + ( $173,710.21 * 4.7846 ) = $3,685,905.60

( X * 433.355 ) = $2,854,773.56

X = $6,587.61

Therefore the Value of Monthly Deposit from Year 16 to 30 = $6,587.61

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