you plan to go back to school for 4yrs . You plan to save 6,400/yr beginning immediately . 4 deposits are made in an account that pays 5.7% interest. How much will you have 4yrs from today
It depends upon how much was deposited each of the four times, what time the deposits were made (at the same time, monthly, quarterly, annually), and if the 5.7% interest is simple or compounded. If compounded is it daily, quarterly, monthly, just what?
Its saving 6,400 per yr
To calculate how much you will have after 4 years, you can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = Total amount after time t
P = Initial principal (deposit)
r = Annual interest rate (in decimal form)
n = Number of times interest is compounded per year
t = Number of years
In this case, the annual interest rate is 5.7% or 0.057 in decimal form. The initial deposit (P) is $6,400, and you will be making 4 deposits in total.
First, let's calculate how much each deposit will accumulate after 4 years:
Deposit 1:
Principal (P1) = $6,400
Interest rate (r) = 0.057
Number of times compounded per year (n) = 1 (assuming interest is compounded annually)
Years (t) = 4
Using the formula:
A1 = P1(1 + r/n)^(nt)
A1 = $6,400(1 + 0.057/1)^(1*4)
A1 = $6,400(1 + 0.057)^4
A1 ≈ $7,958.85
Deposit 2:
Principal (P2) = $6,400
Interest rate (r) = 0.057
Number of times compounded per year (n) = 1
Years (t) = 4
Similarly:
A2 = P2(1 + r/n)^(nt)
A2 = $6,400(1 + 0.057)^4
A2 ≈ $7,958.85
Deposit 3:
Principal (P3) = $6,400
Interest rate (r) = 0.057
Number of times compounded per year (n) = 1
Years (t) = 4
Again:
A3 = P3(1 + r/n)^(nt)
A3 = $6,400(1 + 0.057)^4
A3 ≈ $7,958.85
Deposit 4:
Principal (P4) = $6,400
Interest rate (r) = 0.057
Number of times compounded per year (n) = 1
Years (t) = 4
Once again:
A4 = P4(1 + r/n)^(nt)
A4 = $6,400(1 + 0.057)^4
A4 ≈ $7,958.85
Now, to find the total amount after 4 years, you need to sum up the values of each deposit:
Total amount = A1 + A2 + A3 + A4
Total amount = $7,958.85 + $7,958.85 + $7,958.85 + $7,958.85
Total amount ≈ $31,835.40
Therefore, after 4 years, you will have approximately $31,835.40 in your account.