Answer to Question #123854 in Financial Math for Kierra Jackson

Question

Ricardo is a 30-year-old pack-and -a-half per day smoker who pays $10.49 per pack of cigarettes. Observing an uncle suffering from emphysema, he decides to stop smoking. emphysema, he decides to stop smoking. Assuming an annuity with an interest rate of 5.1% compounded monthly and investing the cost of 45 packs each month.
a) Find the future value when Ricardo is 65
b) Find the amount he can withdraw from his annuity each month for 15 years after he retires.

Answer 1

a)Future value= present value([1+i]ⁿ-1)/i

Present investment value: $10.49* 45 packs=$472.05 per month

interest rate,i:5.1%/100%=0.051 annually, therefore monthly interest rate would be 0.051/12 months=0.00425.

n:frequency of contribution for the 35 years, that is, 35*12 months=420 months

Future value=$472.05( [1+0.00425]⁴²⁰ -1)/0.00425

=$472.05([1.00425⁴²⁰]-1)/0.00425

=$472.05(5.937080938-1)/0.00425

=$472.05(4.937080938/0.00425)

=($472.05*1,161,666103)

= $548,364.484

Future value of annuity=$548,364.48

b ) Pay out annuities=d(1-[1+i]^-Nk )/i

Payout annuities=$548,364.48

d=amount to be withdrawn each month for 15 years

i=0.00425

^-Nk=15 years *12

= 180 months

$548,364.48= d(1- [1+0.00425]^-180 )/0.00425

$548,364.48=d( 1-[1.00425]^-180 )/0.00425

$548,364.48=d(1-0.466088864)/0.00425

$548,364.48=d(0.533911135/0.00425)

$548,364.48=125.6261495 d

$548,364.48/125.6261495=125.6261495 d/125.6261495

$4,365.050447=d

d=$4,365.05