What will be the total amount accumulated when you retire?
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?
Public Comments
- Why? Who wants to know?
- Well one thing to ask is what does "compound continuously" mean? Monthly, quarterly, daily??? Using the Future Value formula for compounded interest, you get really different results depending on how often the interest is compounded. COMPOUNDED MONTHLY (what my bank does): FV = 50000 (1 + i) ^n i = interest divided by total number months per year = .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 (common way some banks do it) FV = 50000 (1+ i)^n i = interest divided by total number quarters per year = =.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 You can make $2662.62 more in 30 years by moving your quarterly compounded interest account to a monthly compouded interest account. If you compound less often than quarterly the amount earned in 30 years will go down, if you compound more often than monthly the amount earned in 30 years will go up drastically. NOTE: ^ symbol is the power symbol
- $50,000 paying 6% annually (compounded daily) will be worth $302,437.63 in 30 years. But if you didn't need it for THIRTY YEARS you could afford to invest it far more aggressively (plenty of time for ups & downs to even out), so a smarter place to put it would be an aggressive growth mutual fund for twenty years, then move the balance to something more conservative for the last few years. This would net you something more like $1.2M (plus or minus $100,000. Both these calculations have a probability of 1. The probability of being struck by lightning is considerably greater than that of winning the lottery! Don't hold your breath!
