Over 2 years, how much more does $2000 in a savings account with an apr of 4.6 compounded semiannually earn in interest than the same amount in a savings account with an apr of 4.4% compounded quarterly? A. $3.76 B. $1.88 C. $7.52 D. $15.04
Mathematics · High School · Wed Jan 13 2021
Answered on
Given:
Principal amount: $2000
Term = 2 years
Compare how much more is earned from 4.6% compounded semiannually than 4.4% compounded quarterly.
The formula for compound interest:
A =P(1 +r/n)^nt
r = rate
n = compounded times
t = term
Solution:
We start solving first 4.6% or 0.046, compounded semiannually.
A =$2000(1 +0.046/2)^(2)(2)
A =$2000(1 +0.023)^4
A = $2190.45
Next we solve 4.4% or 0.04 compounded quarterly.
A =$2000(1 +0.044/4)^(4)(2)
A =$2000(1 +0.011)^8
A =$2000(1 +0.011)^8
A = $2,182.92
Subtract the two amounts to determine the difference.
= $2190.45 - $2182.92
= $7.52
Final answer:
C. $7.52