If you deposit $4,000 at the end of each of the next 20 years into an account paying 11.2 percent interest, you will have $ in the account in 20 years. How much will you have if you make deposits for 40 years? $
Well, with all those deposits, you're definitely making a 'fortune!' But let's calculate it and find out the exact amount.
For the first part, if you deposit $4,000 at the end of each of the next 20 years into an account paying 11.2 percent interest, you can use the future value of an ordinary annuity formula.
The formula is: FV = C * [(1 + r)^n - 1] / r
Where:
FV = Future Value
C = Cash flow per period ($4,000 in this case)
r = Interest rate per period (11.2% divided by 100, so 0.112)
n = Number of periods (20 years)
Calculating it:
FV = 4,000 * [(1 + 0.112)^20 - 1] / 0.112
Please keep in mind that this calculation does not take into account any compounding intervals or any taxes. Also, it assumes you make deposits at the end of each year.
But if you're curious about the amount you'd have after 40 years, you can use the same formula with n = 40.
FV = 4,000 * [(1 + 0.112)^40 - 1] / 0.112
And, voilà! You'll find out just how much you'd have in the account after 40 years of deposits. Enjoy your journey to the 'bank' of the future!
To find out how much you will have in the account after 20 years, we can use the future value of an ordinary annuity formula. The formula is:
FV = P * [(1 + r)^n - 1] / r
Where:
FV = Future Value of the annuity
P = Deposit amount at the end of each year
r = Interest rate per period
n = Number of periods
In this case, P = $4,000, r = 11.2% (or 0.112), and n = 20.
Calculating the future value after 20 years:
FV = $4,000 * [(1 + 0.112)^20 - 1] / 0.112
FV = $4,000 * [(1.112)^20 - 1] / 0.112
Using a calculator, the future value after 20 years is approximately $247,382.08.
Now let's calculate how much you will have if you make deposits for 40 years. The only thing changes here is the value of n which is now 40.
FV = $4,000 * [(1 + 0.112)^40 - 1] / 0.112
FV = $4,000 * [(1.112)^40 - 1] / 0.112
Using a calculator, the future value after 40 years is approximately $2,138,799.35.
Therefore, if you make deposits for 40 years, you will have approximately $2,138,799.35 in the account.
To calculate the future value of the account after 20 years with $4,000 deposited at the end of each year and earning 11.2 percent interest, you can use the formula for the future value of an ordinary annuity.
The formula for the future value of an ordinary annuity is:
FV = P * (((1+r)^n) - 1) / r
Where:
FV is the future value of the annuity
P is the periodic payment (in this case, $4,000)
r is the interest rate per period (in this case, 11.2% or 0.112)
n is the number of periods (in this case, 20 years)
Using the formula, we can calculate the future value of the account after 20 years:
FV = $4,000 * (((1+0.112)^20) - 1) / 0.112
Calculating this expression will give you the future value of the account after 20 years.
To calculate the future value of the account after 40 years, you can use the same formula, but with a different value for n (number of periods).
FV = $4,000 * (((1+0.112)^40) - 1) / 0.112
Calculating this expression will give you the future value of the account after 40 years.
Please note that the calculations assume the interest is compounded annually and there are no other fees or transactions affecting the account balance.