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Estella will deposit $2,000 into an account

that pays 4% annual simple interest. Veronica
will deposit the same amount into a savings
account that pays 4% compound interest,
compounded annually. After 10 years, with
no additional deposits or withdrawals, how
much more will Veronica have earned in
interest than Estella? Round to the nearest
cent.

A.$60.49
B.$160.49
C.$800.00
D.$960.49

User Ryanmoon
by
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1 Answer

1 vote

Final answer:

After calculating simple and compound interest on respective accounts, it is found that Veronica will have earned $160.48 more in interest than Estella after 10 years. The correct answer, rounded to the nearest cent, is B. $160.49.

Step-by-step explanation:

To determine how much more Veronica will have earned in interest with her compound interest account compared to Estella's simple interest account after 10 years, we need to calculate the final amounts for both and then compare the interest earned.

Simple Interest is calculated using the formula: Simple Interest = Principal × Rate × Time.

For Estella's account:
Principal = $2000Rate

= 4% per year (or 0.04 as a decimal)Time

= 10 years
Simple Interest = $2000 × 0.04 × 10

= $800.

Estella's total amount after 10 years will be: Principal + Interest = $2000 + $800

= $2800.

Compound Interest is calculated using the formula: Compound Interest = Principal × (1 + Rate)^Time.

The interest is added to the principal at the end of each compounding period, which in this case is annually.

For Veronica's account:
Principal = $2000Rate

= 4% per year (or 0.04 as a decimal)Time

= 10 years
Compound Interest Total = $2000 × (1 + 0.04)^10

= $2000 × 1.48024

≈ $2960.48.

Finally, we calculate how much more Veronica has earned compared to Estella. Veronica's interest earned is $2960.48 minus her principal of $2000, which is $960.48. Estella earned $800 in interest.

Veronica has earned: $960.48 - $800.00 = $160.48 more in interest than Estella.

Therefore, the answer is B. $160.49 (rounded to the nearest cent).

User Eduard Gamonal
by
8.1k points