Question

Kayin got $1000 from his birthday and Christmas, and Ms. Fernandes decided to put that in a bank account and add $10 a month. Because of the pandemic, Ziya didn’t get to have a birthday party, so she only had $200. Ms. Fernandes decided to deposit it into a bank account that has a continuous monthly interest rate of 5%. After a year, how much more money will Kayin have in his account compared to Ziya?

a) $70
b) $75
c) $80
d) $85

Answer 1

Calculating the final account balances for Kayin and Ziya, considering Kayin's monthly deposits and Ziya's 5% continuous monthly interest,

Step-by-step explanation:

To determine how much more money Kayin will have compared to Ziya after a year, we need to calculate the final amounts in each of their bank accounts. Kayin starts with $1000 and adds $10 a month without any interest, so after a year, Kayin will have:

$1000 + ($10 × 12 months) = $1000 + $120 = $1120.

For Ziya, who starts with $200 and earns a continuous monthly interest rate of 5%, the formula for compound interest is:

P = $200 × (1 + 0.05)^12

Where P is the future value after 12 months. Calculating this gives:

P = $200 × (1.05)^12 = $200 × 1.795856326 = $359.17 (approximately)

Therefore, the difference between Kayin's and Ziya's amounts after a year is:

$1120 - $359.17 = $760.83

Since this value is not given in the answer choices, there is likely a mistake in the interest calculation or understanding of the question. Please recheck the interest rate or the question's details, as continuous monthly interest usually implies using exponential functions for calculations rather than simple multiplication.the difference between their amounts is not matching the provided options. This indicates a possible mistake in the question details or the interest calculation.