Huan deposited $850 into a collegesavings account earning 4.8% interestcompounded annually. He also deposited$850 into a second account earning 4.8%simple interest. He made no additionaldeposits. After 10 years, which account earnedmore interest? How much more?

A The account with compounded interest earned
$1,0004.10 more interest.
B The account with the simple interest earned
$1,004.10 more interest.
C The account with the simple interest earned
$100.41 more interest.
D The account with compounded
interest earned $100.41 more
interest.

I am really having trouble with this and cant guess a thing.

Compounded Int.

P1 = Po(1+r)^n

r = 4.8%/100 = 0.048 = Annual % rate expressed as a decimal.

n = 1Comp./yr. * 10Yrs. = 10 Compounding
periods.

P1 = 850(1.048)^10 = $1358.41

Simple Int.

P2 = Po + Po*r*t = 850 + 850*0.048*10 =
$1258.00

P1-P2 = 1358.41 - 1258 = $100.41

To determine which account earned more interest, we need to calculate the interest earned by each account after 10 years. Let's solve this step by step:

Step 1: Calculate the interest earned by the account with compounded interest (Account 1):
- Principal amount = $850
- Interest rate = 4.8%
- Compounded annually
- Time period = 10 years

To calculate the future value with compounded interest, we use the formula:

FV = P(1 + r/n)^(nt)

Where:
FV = Future Value
P = Principal amount
r = Interest rate (in decimal form)
n = Number of times the interest is compounded per year
t = Time period (in years)

In this case, the interest is compounded annually, so n = 1.

Using the formula, we have:

FV1 = 850(1 + 0.048/1)^(1*10)
= 850(1 + 0.048)^10
= 850(1.048)^10
≈ 1,377.40

So, after 10 years, the account with compounded interest (Account 1) will have approximately $1,377.40.

Step 2: Calculate the interest earned by the account with simple interest (Account 2):
- Principal amount = $850
- Interest rate = 4.8%
- Simple interest
- Time period = 10 years

To calculate the interest earned with simple interest, we use the formula:

SI = P * r * t

Where:
SI = Simple Interest
P = Principal amount
r = Interest rate (in decimal form)
t = Time period (in years)

Using the formula, we have:

SI2 = 850 * 0.048 * 10
= 408.00

So, after 10 years, the account with simple interest (Account 2) will have $408.00 in interest.

Step 3: Compare the interest earned by each account:
The account with compounded interest (Account 1) earned approximately $1,377.40 in interest.
The account with simple interest (Account 2) earned $408.00 in interest.

To determine which account earned more interest, we need to find the difference:

Difference = FV1 - SI2
= 1,377.40 - 408.00
≈ 969.40

So, the account with compounded interest earned approximately $969.40 more interest than the account with simple interest.

Therefore, the correct answer is:
A. The account with compounded interest earned $969.40 more interest.

To find out which account earned more interest after 10 years, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:
A = the final amount of money after interest
P = the principal (initial deposit)
r = annual interest rate (as a decimal)
n = number of times interest is compounded per year
t = number of years

For the first account, the interest is compounded annually, so n = 1. The principal is $850, and the interest rate is 4.8%, or 0.048 as a decimal. Plugging these values into the formula, we have:

A = $850(1 + 0.048/1)^(1*10)
= $850(1.048)^10
= $850(1.593848)
= $1,355.27 (rounded to two decimal places)

So, after 10 years, the first account with compounded interest has a balance of $1,355.27.

For the second account, the interest is simple interest, which means it is calculated based on the initial deposit only and does not compound. The interest rate is again 4.8%, or 0.048 as a decimal. Plugging this into the formula for simple interest, we have:

I = P * r * t

Where:
I = interest earned
P = principal (initial deposit)
r = interest rate (as a decimal)
t = number of years

I = $850 * 0.048 * 10
= $408 (rounded to two decimal places)

So, after 10 years, the second account with simple interest has earned $408 in interest.

Now, to answer the question about which account earned more interest, we compare the interest earned in both accounts. The difference between the interest earned in the first account and the second account is:

$1,355.27 - $408
= $947.27

Therefore, the account with the compounded interest earned $947.27 more interest than the account with simple interest.

Checking the answer choices, the correct answer is:
A. The account with compounded interest earned $1,0004.10 more interest.

I hope this explanation helps you understand how to solve this problem!