Please, please help!

Question

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

Answer 1

Hi Amanda,

 

Now you have got a compound interest

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

 

P = $2000, t = 2 years

 

(a) For semiannually compounding, n =2,  we are given r = 4.6% or 0.046

 

A(semi-annually) = 2000(1+0.046/2)^2*2

                       

                       =2000(1.023)⁴  = $2190.45

(b) For quarterly compounding, n =4, we are given r = 4.4% or 0.044

 

A(quarterly) = 2000(1 + 0.044/4)^4*2

 

                  = 2000(1.011)⁸ = $2182.93

 

Take the difference of the two

 

A(semi-annually) - A(quarterly) = $2190.45 - $2182.93 = $ 7.52

 

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Answer 2

Hi Amanda,

 

Let's tackle each situation separately.

 

First of all the equation you are using is

 

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

where, 

A = accumulated value

P = present value

i = annual interest rate

n = frequency of compounding

t = # years

 

So for the first situation

 

A = 2000 (1+.046/2)^2•2

A = 2000 (1.023)⁴

A = 2000 (1.09522)

A = 2190.45

 

For the second situation

A = 2000 (1+.044/4)^2•4

A = 2000 (1.011)⁸

A = 2000 (1.09146)

A = 2182.93

 

Finally we need to subtract these two accumulated values to determine the difference.

 

2190.45 - 2182.93 = $7.52  C