Uma turned 25 today, that she plans to retire on her 65 th birthday , and that s
ID: 2815514 • Letter: U
Question
Uma turned 25 today, that she plans to retire on her 65 th birthday , and that s he expects to live until her 8 0 th birthday . On her 65th birthday, she wants $ 90,000 and wants that amount to increase by 2 % every year until h er 80th birthday. In other words, she wants to make a withdrawal from her 65th birthday until her 80 th ( including her 80th birthday ). So far, she has managed to save $ 40,000 (until today ) and that money is earning an interest rate of 7% compounded annually . She wants to put additional equal amount of deposit from h er 26th birthday until her 64th birthday in the same account. Given this , how much must she should deposit every year to meet her retirement goal?
A) $2,381.99
B) $3,233.53
C) $2,171.88
D) $2,548.73
E) $1,823.34
Explanation / Answer
First of all we calculate the required PV of the annuity :
Now the PV of the annuity is $28809.88. Interest Rate is 7% and the annuity is for 39 payments. (Starting 26th Bday till 64th Bday).
So as on 25th Bday we can say that,
$2880988 = X/1.07 + X/1.07^2 +X/1.07/3 ............X/1.07^38 + X/1.07^39.
Solving the equation, (We can use a financial cal as well with pv = $28809.88, irr = 7%, n = 39, cpt - PMT),
We get , X = $2171.88 (Ans)
Ans: The deposit every year to meet the retirement goal is $2171.88
Birthday Time line from 64th Bday Cashflow req PV @ 7% from 64th Bday PV 65 1 90000 0.934579439 84112.15 66 2 91800 0.873438728 80181.68 67 3 93636 0.816297877 76434.87 68 4 95508.72 0.762895212 72863.15 69 5 97418.8944 0.712986179 69458.33 70 6 99367.2723 0.666342224 66212.61 71 7 101354.618 0.622749742 63118.56 72 8 103381.71 0.582009105 60169.1 73 9 105449.344 0.543933743 57357.46 74 10 107558.331 0.508349292 54677.2 75 11 109709.498 0.475092796 52122.19 76 12 111903.688 0.444011959 49686.58 77 13 114141.762 0.414964448 47364.77 78 14 116424.597 0.387817241 45151.47 79 15 118753.089 0.36244602 43041.58 80 16 121128.15 0.338734598 41030.3 PV at 64th Bday 962982 PV at 25th Bday (962982/1.07^39) 68809.88 Money Already saved 40000 PV of Annuity 28809.88Related Questions
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