Sam wants to invest the same amount at the end of every 3 months so that he will have 4000 in 3 years. The account will pay 6% compounded quarterly. How much should he deposit each quarter.
To calculate the amount Sam should deposit each quarter, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment
P = the principal amount (the amount Sam needs to deposit each quarter)
r = the annual interest rate (6% or 0.06)
n = the number of times interest is compounded per year (quarterly, so 4)
t = the number of years (3)
We need to find the value of P in this equation when A = $4000. Let's rearrange the formula to solve for P:
P = A / ((1 + r/n)^(nt))
Now we can plug in the values and calculate:
P = 4000 / ((1 + 0.06/4)^(4*3))
Calculating step by step:
Step 1: Calculate (1 + 0.06/4)
= 1 + 0.015
= 1.015
Step 2: Calculate (1.015)^(4*3)
= (1.015)^12
Step 3: Calculate 4000 / (1.015)^12
= 4000 / 1.19561
Step 4: Calculate 4000 / 1.19561
≈ 3342.75
So, Sam should deposit approximately $3342.75 each quarter to have $4000 in 3 years, considering the account's interest rate of 6% compounded quarterly.