Question

Muhammed has money to invest in one of two accounts.Account 1 requires a $2,000 investment for 4 years. It earns 3% interest compounded monthly.Account 2 requires a $2,200 investment for 2 years. It earns 5% interest compounded daily.Which account will earn more interest for Muhammed, and how much?Select the answer that is completely correct.Account 2 earns $232.39 more than Account 1.Account 1 earns $23.30 more than Account 2.Account 1 earns $18.87 more than Account 2.Account 2 earns $176.70 more than Account 1

Answer 1

Given:

Account 1:

Principal, P = $2000

Time, t = 4 years

Rate, r = 3% = 0.03

number of times compounded, n = monthly = 12 months/year

Account 2:

Principal, P = $2200

Time, t = 2 years

Rate, r = 5% = 0.05

number of times compounded, n = daily = 365 days/year

Let's determine the account which will earn more interest.

Apply the compound interest formula:

`I=(P(1+(r)/(n))^(nt))-P`

Where:

P is the Principal

r is the interest rate

n is the number of times the ineterest is compounded per unit time'

t is the time in years

Now, let's find the interest earned in each account.

• ACCOUNT 1:

`\begin{gathered} I=(2000(1+(0.03)/(12))^(12*4))-2000 \\ \\ I=(2000(1+0.0025)^(48))-2000 \\ \\ I=(2000(1.0025)^(48))-2000 \\ \\ I=2254.66-2000 \\ \\ I=254.66 \end{gathered}`

The interest earned in account 1 is $254.66

• ACCOUNT 2:

`\begin{gathered} I=(2200(1+(0.05)/(365))^(730))-2200 \\ \\ I=(2200(1+0.00013698)^(730))-2200 \\ \\ I=2431.36-2200 \\ \\ I=231.36 \end{gathered}`

The interest earned in account 2 is $231.36

We can see the interest earned in account 1 is greater than the interest earned in account 2.

To find the difference, we have:

$254.66 - $231.36 = $23.30

Therefore, Account 1 earns $23.30 more than Account 2.

ANSWER:

Account 1 earns $23.30 more than Account 2.