Question

Trella alcala deposited 1,950 in a new credit union savings account on the first of the quarter the principal earns 4.25 percent interest compound quarterly she made no other deposits or withdrawals

What was the amount in her account at the end of 6 months
What is the compound interest

Answer 1

The amount in her account at the end of 6 months is $1991.58.

The compound interest is $41.58.

Explanation:

The compound interest formula is given by:

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

Where A is the amount of money, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per unit t and t is the time the money is invested or borrowed for.

In this exercise, we have:

`A = 1950, n = 3, r = 0.0425`

What was the amount in her account at the end of 6 months:

This is a when t = 0.5 years.

So

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

`A = 1950(1 + (0.0425)/(3))^(3*0.5) = 1991.58`

The amount in her account at the end of 6 months is $1991.58.

What is the compound interest?

The compound interest is the amount subtracted by the principal. So 1991.58-1950 = $41.58.

Answer 2

Amount in compound interest = p(1 + r/t)^nt where p is the initial deposit, r = rate, t = number of compunding in a period and n = period.

Here, Amount after 6 months (0.5 year) = 1,950(1 + (4.25/100)/4)^(0.5 x 4) = 1,950(1 + 0.0425/4)^2 = 1,950(1 + 0.010625)^2 = 1,950(1.010625)^2 = 1,950(1.0213629) = $1,991.66

Compound interest = Amount - principal (initial deposit) = $1,991.66 - $1,950 = $41.66