Question

Over two years, how much more does $2000 in a savings account with an APR of 4.6% compounded semiannually earn interest than the same amount in a savings account with an APR of 4.4% compounded quarterly?

A. $15.04

B. $3.76

C. $1.88

D. $7.52

Answer 1

Dont wanna do the work, i got you: $7.52

Answer 2

The account of 4.6 compounded semiannually earn $7.52 more than the account of 4.4% compounded quarterly.

What is the percentage?

A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate the percent of a number, divide the number by the whole and multiply by 100.

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 :

$\rm A=P(1+\dfrac{r}{n})^{nt}\\\\A=2000(1+\dfrac{4.6}{100}^{2 \times 2}\\\\A=2000(1+\dfrac{4.6}{100})^{2 \times 2}\\\\A=2190.45$

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 :

$\rm A=P(1+\dfrac{r}{n})^{nt}\\\\A=2000(1+\dfrac{0.044}{4})^{4 \times 2}\\\\ A =2182.93$

The difference = 2190.45 - 2182.93 = 7.52

Hence, The account of 4.6 compounded semiannually earn $7.52 more than the account of 4.4% compounded quarterly.

Learn more about percentage here;

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