Question

Andrea Gilford's savings account has a balance of $169. After 2 years, the amount of interest at 12% compounded quarterly will be $ .



C. The stories told by los viejitos inspired Anaya's love of words and books.

Answer 1

Have you considered calculating it?

Annual Interest is 12%
Quarterly Interest is 12% / 4 = 3%

Go!

Answer 2

12% Quarterly interest = [(1 + r/n)^1/n]-1
Where 'n' is number of compounding periods. (in this case it's 4)

[(1 + .12/4) ^ 4]-1
=1.12550881 -1
=12.550881 annual interest

Answer 3

Why in the name of reason do we want the annual interest rate?

Let's just solve the problem directly.

\(169 - 169(1.03)^{8} =\;??\)

Answer 4

Whoops! Other way around.

Answer 5

total amount = principal * (1 +r)^n
total amount = 169 * (1.12550881)^2
total amount = 169*1.2667700814
total amount = 214.08
calculator to check your work:
http://www.1728.org/compint.htm

Answer 6

We want the annual rate because that is what the quarterly compounding will yield.

Answer 7

If we use the formula
total = 169 * (1+r/n)^n2
where n is the number of compounding periods per year and n2 is years * n,
we get the same answer $214.08
However we have to remember with this formula, we need to use 2 values of 'n'.
total = 169 * (1+12/4)^8