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

Answer 1

First of all we calculate the required PV of the annuity :

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				28809.88

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