How much money must you deposit now at 6% interest compounded quarterly in order to be able to withdraw $5000 at the end of each quarter for five years?
PV = 500( 1 - 1.015^-20)/.015
= .....
To calculate the amount of money you must deposit now, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the deposits ($5000 * 4 quarters * 5 years = $100,000)
P = the principal amount (the initial deposit we need to find)
r = the annual interest rate (6% or 0.06)
n = the number of times interest is compounded per year (quarterly = 4)
t = the number of years (5)
We want to solve for P, so we can rearrange the formula:
P = A / (1 + r/n)^(nt)
Now let's substitute the values into the formula:
P = $100,000 / (1 + 0.06/4)^(4*5)
Let's simplify it step by step:
1 + 0.06/4 = 1.015
4 * 5 = 20
Now we can continue simplifying:
P = $100,000 / (1.015)^20
Using a calculator, we can find the value for (1.015)^20:
(1.015)^20 ≈ 1.3486
Finally, we can calculate the principal amount:
P = $100,000 / 1.3486
P ≈ $74,187.53
Therefore, you need to deposit approximately $74,187.53 now in order to be able to withdraw $5000 at the end of each quarter for five years, with a 6% interest rate compounded quarterly.