Theo deposited $1,250 in a savings account that pays 6% interest,
compounded quarterly. What was his balance at the end of the second
quarter after the interest had been added?
Actually the first steps are right except with compound interest you earn interest on interest, so just adding another 18.75 would not solve it. You have to account for the interest you earn the 1st quarter. So I got 1287.78
Amount = 1250(1 + .015)^2
= 1287.78
1250 * 0.06 = $75 yearly interest
75 / 4 = $18.75 first quarter interest
1250 + 18.75 = $1,268.75 balance at the end of the first quarter
Repeat the above steps to find the balance after the second quarter.
To calculate Theo's balance at the end of the second quarter after interest, we need to use the formula for compound interest:
A = P(1 + r/n)^(nt)
where:
A = the balance after time t
P = the principal amount (initial deposit) = $1,250
r = annual interest rate (in decimal form) = 6% = 0.06
n = number of times interest is compounded per year = quarterly, which means 4 times
t = time in years = 2 quarters, which is 2/4 = 0.5 years
Plugging in the values into the formula:
A = 1250(1 + 0.06/4)^(4*0.5)
Now, let's solve the equation step by step.
A = 1250(1 + 0.015)^(2)
First, simplify the expression within the parentheses:
A = 1250(1.015)^(2)
Next, square the expression within the parentheses:
A = 1250(1.030225)
Finally, multiply the result by the principal amount (1250):
A = $1,288.78
Therefore, Theo's balance at the end of the second quarter after the interest had been added is $1,288.78.