Buddy Bolly just received his annual bank statement. One year ago, Buddy deposited $10,000 in a savings account. Today, his balance is $10,509.45. Buddy's savings account interest is compounded quarterly. Buddy received an annualized interest rate of __________ percent.
A) 6
B) 5
C) 4
D) 3

Question

Quizplus · Accepted Answer

To find the annualized interest rate, we can use the formula:

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

where:
A = the ending balance ($10,509.45)
P = the principal (initial deposit of $10,000)
r = the annual interest rate (what we want to solve for)
n = the number of times interest is compounded per year (4, since it's compounded quarterly)
t = the number of years (1)

Plugging in the values we know, we get:

$10,509.45 = $10,000(1 + r/4)^(4*1)

Simplifying:

1.050945 = 1 + r/4

0.050945 = r/4

r = 0.20378 (rounded to 5 decimal places)

Multiplying by 100 to get a percentage:
r = 20.378%

Rounding to the nearest whole number gives us a final answer of:

B) 5

Buddy Bolly Just Received His Annual Bank Statement