Ben deposits $400 into an account that earns 5% interest compounded annually. Sam deposits the same amount into an account that earns 5% simple interest. Compare the account balances after 2 years.
Simple interest
400(.05)(2) = $40
compound
400(1.05)^2
To compare the account balances after 2 years, we need to calculate the balance for each account.
For Ben's account with compound interest, the formula to calculate the future value is:
FV = P * (1 + r)^n
Where:
FV = future value
P = principal amount (initial deposit)
r = interest rate (expressed as a decimal)
n = number of compounding periods
In this case, Ben deposited $400, the interest rate is 5% (or 0.05 as a decimal), and the compounding is done annually for 2 years.
Using the formula, we can calculate Ben's future value:
FV_ben = $400 * (1 + 0.05)^2
FV_ben = $400 * 1.1025
FV_ben = $441
So after 2 years, Ben's account balance with compound interest will be $441.
For Sam's account with simple interest, the formula to calculate the future value is:
FV = P * (1 + r * n)
Where:
FV = future value
P = principal amount (initial deposit)
r = interest rate (expressed as a decimal)
n = number of compounding periods
In this case, Sam also deposited $400, and the interest rate is 5% (or 0.05 as a decimal), but the interest is calculated only once per year.
Using the formula, we can calculate Sam's future value:
FV_sam = $400 * (1 + 0.05 * 2)
FV_sam = $400 * 1.1
FV_sam = $440
So after 2 years, Sam's account balance with simple interest will be $440.
Comparing the two account balances, we see that Ben's account with compound interest ($441) has a slightly higher balance than Sam's account with simple interest ($440).