Mr. Smith wants to save for his son's college education. If he deposits $400 each month at 3% compounded monthly, how much will he have in the account after 48 months?
To calculate the amount Mr. Smith will have in the account after 48 months, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount in the account
P = the initial deposit or principal amount
r = the annual interest rate (in decimal form)
n = the number of times the interest is compounded per year
t = the number of years
In this case:
P = $400 (monthly deposit)
r = 3% = 0.03 (annual interest rate)
n = 12 (compounded monthly)
t = 48 months
First, we need to convert the annual interest rate into a monthly interest rate by dividing it by 12 since the interest is compounded monthly:
monthly interest rate = 0.03 / 12 = 0.0025
Now, we can substitute these values into the formula to calculate the final amount:
A = 400(1 + 0.0025)^(12 * 4)
Now we can solve the equation:
A = 400(1 + 0.0025)^(48)
A ≈ 400(1.0025)^(48)
A ≈ 400(1.128)
Using a calculator or spreadsheet, we can find that A ≈ $451.20.
Therefore, Mr. Smith will have approximately $451.20 in the account after 48 months.
surely you have the formula for the future value of such a cash stream. If not, here's a site with the formula and a calculator.
http://keisan.casio.com/exec/system/1234231998