Question

Help pleeeeease
Theo deposited $1,250 in a savings account that pays 6% interest, compound quarterly. What was his balance at the end of the second quarter after the interest had been added?
A. $1,270.31
B. $1,270.65
C. $1,290.62
D. $1,287,78
Please explain your answer clearly! and explain how you got it!

Answer 1

The account pays 6% interest per year.
The interest is compounded quarterly, or 4 times per year. That means at the end of each quarter year (3 months), he gets 3-months worth of interest added to the principal amount.
Since the interest is added each quarter, and since the yearly interest rate is 6%, the interest earned in 1 quarter is 6%/4 =1.5%. In 1 quarter (3 months), he earns 1.5%.

Start with $1250.
At the end of the first quarter, he earned 1.5% interest.
$1250 + 1.5% * $1250 = $1250 + 0.015 * $1250 = $1250 + $18.75 =
$1268.75
At the end of the first quarter he now has $1268.75.

Now he will earn interest for the second quarter.
He starts with $1268.75 and will earn 1.5% interest on that.
We do the same calculation we did above, but we start with $1268.75.
$1268.75 + 1.5% * $1268.75 = $1268.75 + 0.015 * $1268.75 = $1268.75 + $19.03 = $1287.78

The answer is $1287.78

Answer 2

There are 4 quarters in a year
Each quarter=3 months
So balance at the end of the second quarter means the balance after 6 months
The formula to find the balance is
A=p (1+r/k)^kt
A the balance?
P initial deposited 1250
R interest rate 0.06
K compounded quarterly 4
T time 6months/12months
Plug in the formula
A=1250 (1+0.06/4)^(4×(6/12))
A=1250 (1+0.06/4)^(2)
A=1287.78

So the answer is d
Hope it helps!