Rachel and Ross’s brief one night encounter produced a lovely daughter Emma, who was born on October 31st. Both parents are excited and they are eager to make sure Emma doesn’t get saddled with college bills. Rachel suggests, as a birthday present, that they each deposit $3,000 a year for 6 years, starting with Emma’s first birthday. Ross is still thinking about his car payment so he suggested waiting until Emma is six and then every year until Emma turns 18, both he and Rachel would contribute $3,000 each (11 payments). Assume that Emma can earn 7% on her account. Is Ross’s plan better than Rachel’s or is Rachel’s plan better, By how much is one plan better?
1. Rachels plan.
Formula: The Future Value of an ordinary annuity (FV)
FV7= C× {[(1+r)^n]-1}/r
FV7 = Future value (The cumulative amount available at the end
of 7 years)
C= Periodic cash outflow. 3000
r =effective interest rate for the period. 7%
n = number of periods. 6
FV7= 3000× {[(1+0.07)^6]-1}/0.07
FV7 = $21,459.87
(Balance at the end of 7 years).
FV18 = FV7(1+r)^n
n = 11years.
FV18= $21,459.87(1.07)^11
FV18 = $45,169.85
Balance at the end of 18 years as per Rachels plan = $45,169.85
2. Formula: The Future Value of an ordinary annuity (FV)
FV18= C× {[(1+r)^n]-1}/r
FV18 = Future value (The cumulative amount available at the end
of 18 years)
C= Periodic cash outflow. 3000
r =effective interest rate for the period. 7%
n = number of periods. 11
FV7= 3000× {[(1+0.07)^11]-1}/0.07
FV7 = $47,350.80
(Balance at the end of 7 years).
Balance as per Ross plan = $47,350.80
Conclusion: Ross plan is better than Rachaels plan.
It is better by $2,180.95
Rachel and Ross’s brief one night encounter produced a lovely daughter Emma, who was born on...
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