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Step2247 [10]
2 years ago
10

Jack invested $7,600 in an account paying an interest rate of 6\tfrac{1}{4}6 4 1 ​ % compounded continuously. John invested $7,6

00 in an account paying an interest rate of 6\tfrac{3}{4}6 4 3 ​ % compounded quarterly. After 19 years, how much more money would John have in his account than Jack, to the nearest dollar?
Mathematics
2 answers:
kramer2 years ago
8 0

Answer: John would have $1371.33 more in his account than Jack.

Step-by-step explanation:

Formula to calculate amount after t years if compounded continuously:

A=Pe^{rt}

Formula to calculate amount after t years if compounded quarterly:

A=P(1+\dfrac{r}{4})^{4t}

, where P= Principal amount, r= rate of interest.

Given: P= $7,600

t=19 years

For Jack, r=6\dfrac{1}{4}\%=\dfrac{25}{4}\%=\dfrac{25}{400}=0.0625

For John, r=6\dfrac{3}{4}\%=\dfrac{27}{4}\%=\dfrac{27}{400}=0.0675

Amount in Jack's account after 19 years= 7600e^{0.0625(19)}

=7600e^{1.1875}\\\\=7600(3.27887376794)\\\\\approx\$24,919.44

Amount in John's account after 19 years= 7600e^{0.0675(19)}

=7600(1+0.0675)^{19}\\\\=7600(3.45931245291)\\\\\approx\$26,290.77

Difference = 26290.77-24919.44 = $ 1,371.33

John would have $1371.33 more in his account than Jack.

s2008m [1.1K]2 years ago
6 0

Answer:668

Step-by-step explanation: I just did it.

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