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?​

Answer 1

$7.52

Explanation:

Answer 2

Final answer is $7.52.

Explanation:

Given that initial amount P = $2000

Interest rate r = 4.6% = 0.046

Number of compounding periods per year = n = 2 {semiannually}

Time = 2 years

Then future value is given by :

`A=P\left(1+(r)/(n)\right)^(n\left(t\right))`

`A=2000\left(1+(0.046)/(2)\right)^(2\left(2\right))=2190.45`

Similarly calculate future value for 2nd case:

Given that initial amount P = $2000

Interest rate r = 4.4% = 0.044

Number of compounding periods per year = n = 4 {quarterly}

Time = 2 years

Then future value is given by :

`A=P\left(1+(r)/(n)\right)^(n\left(t\right))`

`A=2000\left(1+(0.044)/(4)\right)^(4\left(2\right))=2182.93`

then difference = 2190.45 - 2182.93 = 7.52

Hence final answer is $7.52.