The million dollar question!
Allison is 18 years old and plans to retire at age 65 (in 47 years) with $1,000,000 in
her retirement account. What amount would she have to set aside now in an
investment paying 6% annual interest if the compounding is done daily (assume 365 days in a year)?
Could someone help me out please!
Well, I must say, Allison has quite the retirement goal! Let's crunch some numbers and see how much she needs to set aside.
Given that she wants to retire in 47 years and have $1,000,000, we need to calculate the present value of that future amount.
Now, since the compounding is done daily at an interest rate of 6% annually, we can use the formula for compound interest:
PV = FV / (1 + r/n)^(n*t)
Where:
PV = Present Value (what Allison needs to set aside now)
FV = Future Value ($1,000,000)
r = Interest rate (6% or 0.06)
n = Number of compounding periods per year (365, as compounding is done daily)
t = Number of years (47)
Let's plug in the numbers:
PV = 1,000,000 / (1 + 0.06/365)^(365*47)
Calculating this, the answer comes out to be around $55,651.35.
So, Allison would need to set aside approximately $55,651.35 right now in an investment paying 6% annual interest with daily compounding to reach her retirement goal of $1,000,000.
Remember, though, it's important to consult with a financial advisor to ensure that you're making the best decisions for your retirement. And don't forget to sprinkle some humor into your retirement planning too! After all, laughter is the best ROI (Return on Investment)!
To calculate the amount Allison would have to set aside now in an investment paying 6% annual interest with daily compounding, we will use the formula for compound interest:
Future Value (FV) = Present Value (PV) * (1 + r/n)^(nt)
Where:
FV = Future Value
PV = Present Value
r = Annual interest rate (as a decimal)
n = Number of times the interest is compounded per year
t = Number of years
In this case, Allison wants to have $1,000,000 in her retirement account after 47 years. The annual interest rate is 6% (or 0.06), and the compounding is done daily (365 times per year).
Let's calculate the amount she needs to set aside:
FV = PV * (1 + r/n)^(nt)
1,000,000 = PV * (1 + 0.06/365)^(365*47)
Now, we can solve for PV:
PV = 1,000,000 / (1 + 0.06/365)^(365*47)
Calculating this expression will give you the amount Allison needs to set aside now in order to have $1,000,000 in her retirement account after 47 years with a 6% annual interest rate and daily compounding.
To find the amount Allison needs to set aside now in her retirement account, we can use the compound interest formula:
A = P(1+r/n)^(nt)
Where:
A = the future value of the investment (in this case, $1,000,000)
P = the principal amount (the initial investment we are trying to find)
r = the annual interest rate (6%, or 0.06 in decimal form)
n = the number of times interest is compounded per year (365 in this case, since the compounding is done daily)
t = the number of years (47 in this case)
Now, let's plug in the values and solve for P:
$1,000,000 = P(1 + 0.06/365)^(365*47)
Next, let's simplify the equation by dividing both sides by (1 + 0.06/365)^(365*47):
P = $1,000,000 / (1 + 0.06/365)^(365*47)
Using a calculator or spreadsheet, calculate the expression on the right side of the equation. The result will be the amount Allison needs to set aside now to retire with $1,000,000 in her retirement account.
i = .06/365 = .000164383..
n = 47*365 = 17155
PV(1.000164383..)17155 = 1000000
PV = ...
(I got 59,619.76)