Question

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 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? A $672.13 B $695.00 C $694.25 D $694.51 Mathematics

Answer 1

To find the total balance of both accounts at the end of 2 years, we calculate simple interest for Account I and expect compound interest for Account II. The total balance will be more than $428 + $250 = $678, making option B ($695.00) the closest amount.

Step-by-step explanation:

To find the total balance of both accounts at the end of 2 years, we need to calculate the interest for each account and add it to the initial deposit.

For Account I, the interest is calculated using simple interest formula: Interest = Principal * Rate * Time. So, the interest earned in 2 years is $400 * 0.035 * 2 = $28. Therefore, the total balance in Account I after 2 years is $400 + $28 = $428.

For Account II, the interest is compounded annually. Since we don't have the exact interest rate, we cannot calculate the exact value. However, we know that the interest will be higher than simple interest. Based on the example given in the reference materials, the compound interest after 3 years for a $100 deposit at an interest rate of 5% is $15.76. We can expect the interest for the $250 deposit in Account II to be higher. Therefore, the total balance in Account II after 2 years will be more than $250.

Combining the balances in both accounts, the total balance at the end of 2 years will be more than $428 + $250 = $678. Therefore, the closest amount to the total balance is $695.00, which is option B.

Answer 2

The initial amount is $650. The $400 is deposited in Account 1 with 3.5% annual simple interest. The $250 is deposited in Account 2 with 3.5% interest compounded monthly.
n = 2 years
Account 1: Simple Interest

F = P (1+rn)
= 400 (1 +(0.035*2))
= $428

Account 2: Compound Interest

F = P (1+i)^n
= 250 ( 1+0.035)^2
F = 267.81

Total money after 2 years = $428 + $267.81
T = $695.81