Question

Vanessa deposits $24,000 into each of two savings accounts. Account I earns 2. 4% interest compounded annually. Account II earns 2. 4% annual simple interest. There are no additional deposits or withdrawals. What is the sum of the balances of these accounts at the end of 5 years? $53,760. 00 $53,901. 59 $54,043. 20 $56,640. 0.

Answer 1

The sum of the balances of these accounts at the end of 5 years is given by: Option B: $53,901.59 (approx)

How to calculate compound interest's amount?

If the initial amount (also called as principal amount) is P, and the interest rate is R% per unit time, and it is left for T unit of time for that compound interest, then the interest amount earned is given by:

$CI = P(1 +\dfrac{R}{100})^T - P$

The final amount becomes:

$A = CI + P\\A = P(1 +\dfrac{R}{100})^T$

How to calculate simple interest amount?

If the initial amount (also called as principal amount) is P, and the interest rate is R% annually, and it is left for T years for that simple interest, then the interest amount earned is given by:

$I = \dfrac{P \times R \times T}{100}$

For the considered case, we're given that:

• Initial amount in both accounts deposited = $24,000 = P
• Type of interest: Compound interest in first account and simple interest in second account
• Unit of time: Annually
• Rate of interest = 2.4% annually = R
• Total unit of time for which amount is to be calculated: 5 years = T

In first account, the final amount at the end of 5 years is evaluated as:

$A = 24000(1 + \dfrac{2.4}{100})^4 = 24000(1.024)^4 \approx 27021.59\: \rm (in \: dollars)$

In second account,  the final amount at the end of 5 years is evaluated as:

$A = 24000 + \dfrac{24000 \times 2.4 \times 5}{100} = 24000 + 2880 = 26880 \text{\: (in dollars)}$

Total amount after 5 years in these accounts = $27021.59 + 26880 = 53901.59$ (in dollars)

Thus, the sum of the balances of these accounts at the end of 5 years is given by: Option B: $53,901.59 (approx)

Learn more about compound interest here:

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