Compound word problem
Sarah decides to open up her own bank account for her schooling and wants to save money. She decides to put $500.00 in the savings account she is opening. The amount she earns has 8% interest and it’s compounded quarterly. How much would Sarah have in her account after a two year span of saving money?
i = .08/4 = .02
n = 4(2) = 8 quarters
amount = 500(1.02)^8
= .....
To calculate the amount of money Sarah will have in her account after a two-year span, we can use the formula for compound interest:
A = P(1 + r/n)^(nt),
where:
A = final amount
P = initial principal (the amount Sarah is putting in the account), which is $500.00
r = annual interest rate, expressed as a decimal, which is 8% or 0.08
n = number of times the interest is compounded per year, which is quarterly, so it's 4
t = number of years, which is 2
Now we can substitute these values into the formula and calculate the final amount:
A = 500(1 + 0.08/4)^(4*2).
First, let's calculate the interest rate per quarter: 0.08/4 = 0.02.
Now, let's calculate the exponent: 4*2 = 8.
Finally, let's substitute these values into the formula and calculate:
A = 500(1 + 0.02)^8.
A = 500(1.02)^8.
Using a calculator, we can calculate that (1.02)^8 is approximately 1.171661.
A = 500 * 1.171661.
A ≈ $585.83.
So, Sarah would have approximately $585.83 in her account after a two-year span of saving money with an 8% interest compounded quarterly.