Your bank pays 9% interest, compounded annually. Use the appropriate formula to find how much you should deposit now to yeild an annuity payment of $800 at the END of each year, for 10 years?
PV = 800( 1 - 1.09^-10)/.09
Wow, let me know which bank pays you 9% in 2014.
To find the amount you should deposit now to yield an annuity payment of $800 at the end of each year for 10 years, you can use the formula for the present value of an ordinary annuity:
P = A * (1 - (1 + r)^(-n)) / r
Where:
P is the present value (the amount you should deposit now)
A is the annuity payment ($800)
r is the interest rate per period (9% or 0.09)
n is the number of periods (10 years)
Let's plug the values into the formula:
P = 800 * (1 - (1 + 0.09)^(-10)) / 0.09
Now, let's solve the equation step-by-step:
1. Calculate the part inside the parentheses:
(1 + 0.09) = 1.09
2. Calculate the negative exponent inside the parentheses:
(-10) = -1
3. Use the power rule to simplify the negative exponent:
(1.09)^(-10) ≈ 0.4220386807
4. Calculate (1 - (1.09)^(-10)):
(1 - 0.4220386807) ≈ 0.5779613193
5. Substitute the calculated values into the formula:
P = 800 * (0.5779613193) / 0.09
6. Perform the multiplication:
P ≈ 800 * 6.42
7. Calculate the final result:
P ≈ $5,136
Therefore, you should deposit approximately $5,136 now to yield an annuity payment of $800 at the end of each year for 10 years, assuming a 9% interest rate compounded annually.
To find the amount you should deposit now to yield an annuity payment of $800 at the end of each year for 10 years, you can use the formula for the present value of an ordinary annuity:
PV = (PMT / r) * (1 - (1 + r)^(-n))
Where:
PV = Present value (the amount you should deposit now)
PMT = Payment per period ($800 in this case)
r = Interest rate per period (9% or 0.09 as a decimal, compounded annually)
n = Number of periods (10 years in this case)
Now let's plug in the values and calculate:
PV = (800 / 0.09) * (1 - (1 + 0.09)^(-10))
PV = (800 / 0.09) * (1 - (1.09)^(-10))
Using a calculator:
PV ≈ (800 / 0.09) * (1 - 0.4223821008)
PV ≈ 8888.88888889 * 0.5776178992
PV ≈ 5128.38973145
So, you should deposit approximately $5128.39 now to yield an annuity payment of $800 at the end of each year for 10 years, given an interest rate of 9%, compounded annually.