Nicolas has $650 to deposit into two different savings accounts.
Nicolas will deposit $400 into Account I, which earns 3.5% annual simple interest.
He will deposit $250 into Account II, which earns 314% interest compounded annually.
Nicolas will not make any additional deposits or withdrawals. Which amount is closest to the total balance of these two accounts at the end of 2 years?
sneaking suspicion you mean 3.14%
250(1 + 0.0314)^2
dang!
well, I at least knew it wasn't 314%
To calculate the total balance of the two accounts at the end of 2 years, we need to calculate the balance for each account separately and then add them together.
Let's start with Account I, which earns simple interest. The formula to calculate the balance after a given time period with simple interest is:
Balance = Principal + (Principal * Interest Rate * Time)
In this case, the principal (amount deposited) for Account I is $400, the interest rate is 3.5% (or 0.035), and the time is 2 years. Plugging in these values into the formula:
Balance Account I = $400 + ($400 * 0.035 * 2)
= $400 + ($400 * 0.07)
= $400 + $28
= $428
So, the balance for Account I at the end of 2 years is $428.
Now let's move on to Account II, which earns compound interest. The formula to calculate the balance after a given time period with compound interest is:
Balance = Principal * (1 + Interest Rate) ^ Time
In this case, the principal for Account II is $250, the interest rate is 314% (or 3.14), and the time is 2 years. Plugging in these values into the formula:
Balance Account II = $250 * (1 + 3.14) ^ 2
= $250 * (1 + 3.14) * (1 + 3.14)
= $250 * 4.14 * 4.14
= $250 * 17.1396
= $4284.9 (approximated to the nearest cent)
So, the balance for Account II at the end of 2 years is approximately $4284.9.
Finally, to calculate the total balance of these two accounts at the end of 2 years, we add the balances of Account I and Account II:
Total Balance = $428 + $4284.9
= $4712.9 (approximated to the nearest cent)
Therefore, the amount closest to the total balance of these two accounts at the end of 2 years is approximately $4712.9.
400(1+0.035*2)
250(1 + 0.314)^2