Question

Sophie invested $12,000 into a fund earning 6.50% compounded monthly. She plans to withdraw $850 from the fund at the end of every quarter. If the first annuity withdrawal is to be made 4 years from now, how long will it take for the fund to be depleted?

Express the answer in years and months, rounded to the next period

Answer 1

Solution :-

Interest rate per month = 6.50% / 12 = 0.5417%

Interest Rate per quarter = ( 1 + 0.005417 )³ - 1 = 0.01634 = 1.634%

Now the Value of Investment after 15 Quarters = $12,000 * ( 1 + 0.01634 )¹⁵

= $12,000 * 1.2752

= $15,302.24

Now the quarterly Withdrawal = $850

Now , = $15,302.24 = $850 * PVAF ( 1.634% , n )

= 18.00263 = [ 1 - ( 1 + 0.01634 )^-n ] / 0.01634

0.29413 = 1 - ( 1 + 0.01634 )^-n

( 1 + 0.01634 )^-n = 0.70587

( 1 + 0.01634 )ⁿ = 1.41669

take log Both sides

n log ( 1.01634 ) = log ( 1.41669 )

n = 21.49 quarters

= 5 Years 4.5 months

Therefore 5 Years 4.5 months from the first withdrawal , and 9 years 3 months ( approx ) from the investment

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answered by: anonymous