Question

Liam deposits $3,500 in saving account that pays 0.8% interest, compounded quarterly. Round each answer to the nearest cent.

a. Find the first quarter's interest.
b Find the first quarter's ending balance.
Find the second quarter's interest.
D
d, Find the second quarter's ending balance.
e. Find the third quarter's interest.
Find the third quarter's ending balance.
8 Find the fourth quarter's interest.
h. What is the balance at the end of one year?
How much interest does the account earn in the first year?

Answer 1

a. First quarter's interest:

Interest is calculated using the formula: A = P(1 + r/n)^(nt), where:

- P is the principal amount ($3,500)

- r is the annual interest rate (0.8% or 0.008 as a decimal)

- n is the number of times interest is compounded per year (quarterly, so 4 times)

- t is the time the money is invested for (1 quarter, so 1/4 year)

Plugging these values into the formula:

A = 3,500 * (1 + 0.008/4)^(4*(1/4))

A = 3,500 * (1 + 0.002)^1

A = 3,500 * (1.002)^1

A = 3,500 * 1.002

A = 3,507

So, the first quarter's ending balance is $3,507, and the interest earned in the first quarter is $3,507 - $3,500 = $7.

b. Second quarter's interest:

Now, you'll use the same formula, but with a new principal (the first quarter's ending balance):

P = $3,507

A = 3,507 * (1 + 0.008/4)^(4*(1/4))

A = 3,507 * (1.002)^1

A = 3,507 * 1.002

A = 3,513.51

The second quarter's ending balance is $3,513.51, and the interest earned in the second quarter is $3,513.51 - $3,507 = $6.51.

Repeat this process for the third and fourth quarters to find the third quarter's ending balance and interest, as well as the fourth quarter's ending balance and interest.

c. Third quarter's interest:

P = the ending balance from the second quarter

d. Third quarter's ending balance:

e. Fourth quarter's interest:

P = the ending balance from the third quarter

f. Fourth quarter's ending balance:

After calculating all four quarters, sum up the interest earned in each quarter to find the total interest earned in the first year, and add it to the ending balance from the fourth quarter to find the balance at the end of one year.

Step-by-step explanation:

Answer 2

Liam will earn $28.08 in interest during the first year on his $3,500 deposit with an annual interest rate of 0.8%, compounded quarterly. He will see his account balance grow each quarter, with an ending balance of $3,528.08 at the end of one year.

Step-by-step explanation:

To calculate the interest earned on a savings account with compound interest, we use the formula A = P(1 + r/n)(nt), where A is the amount of money accumulated after n years, including interest, P is the principal amount, r is the annual interest rate (decimal), n is the number of times interest is compounded per year, and t is the time in years.

For Liam's deposit of $3,500 at an interest rate of 0.8% compounded quarterly:

• Quarterly interest rate (r/n) = 0.008/4 = 0.002.
• Number of times compounded in a quarter (nt) = 4 * (1/4) = 1.

1. First quarter's interest = 3500 * (1 + 0.002)^1 - 3500 = $7.00.
2. First quarter's ending balance = 3500 + 7.00 = $3,507.00.
3. Second quarter's interest = 3507 * (1 + 0.002)^1 - 3507 = $7.01.
4. Second quarter's ending balance = 3507 + 7.01 = $3,514.01.
5. Third quarter's interest = 3514.01 * (1 + 0.002)^1 - 3514.01 = $7.03.
6. Third quarter's ending balance = 3514.01 + 7.03 = $3,521.04.
7. Fourth quarter's interest = 3521.04 * (1 + 0.002)^1 - 3521.04 = $7.04.
8. End of year balance = 3521.04 + 7.04 = $3,528.08.
9. Total interest earned in first year = 3,528.08 - 3500 = $28.08.