Say that you won a lottery prize of 50000 and decided to sav

Say that you won a lottery prize of $50,000 and decided to save it for your retirement in 30 years in an interest bearing account which compounds continuously at 6.0%. What will be the total amount accumulated when you retire?

Solution

Using the Future Value formula for compounded interest, you get really different results depending on how often the interest is compounded.

COMPOUNDED MONTHLY:

FV = 50000 (1 + i) ^n
i = interest divided by total number months per year = 0.06 /12 = 0.005
n = number years times number of months per year = 30 * 12 = 360
FV = 50000 (1+ 0.005) ^ 360
FV = 50000 (6.0225752122) = $301128.76

COMPOUNDED QUARTERLY:
FV = 50000 (1+ i)^n
i = interest divided by total number quarters per year = 0.06 / 4 = 0.015
n = number years times number of quarters per year = 30 * 4 = 120
FV = 50000 (1+ 0.015) ^ 120
FV = 50000 (5.5993228723) = $298466.14

COMPOUNDED YEARLY:
FV = 50000 (1+ i)^n
i = interest divided by total number quarters per year = 0.06 / 1 = 0.06
n = number years times number of quarters per year = 30 * 1 = 30
FV = 50000 (1+ 0.06) ^ 30
FV = 50000 (5.74349117291) = $ 287174.558646