Mathematics: Over 2 years, how much more does $2000 in a savings account with an aprof 4.6% compounded semiannually earn in interest than the same amount ina savings account with an apr of 4.4% compounded quarterly?

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Over 2 years, how much more does $2000 in a savings

randall10

10.03.2022

Final answer is $7.52.

Step-by-step 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 :

$A=P\left(1+\frac{r}{n}\right)^{n\left(t\right)}$

$A=2000\left(1+\frac{0.046}{2}\right)^{2\left(2\right)}=2190.45$

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 :

$A=P\left(1+\frac{r}{n}\right)^{n\left(t\right)}$

$A=2000\left(1+\frac{0.044}{4}\right)^{4\left(2\right)}=2182.93$

then difference = 2190.45 - 2182.93 = 7.52

Hence final answer is $7.52.

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