QuestionJuly 22, 2025

Trish invests 5,000 in her IRA in a bond trust that pays 7% interest compounded quarterly. Sean invests 5,000 in his IRA in a certificate of deposit that pays 6.9% compounded continuously. Who has more money after 20 years,Trish or Sean? After 20 years, Trish will have Ssquare . (Round to the nearest cent as needed.)

Trish invests 5,000 in her IRA in a bond trust that pays 7% interest compounded quarterly. Sean invests 5,000 in his IRA in a certificate of deposit that pays 6.9% compounded continuously. Who has more money after 20 years,Trish or Sean? After 20 years, Trish will have Ssquare . (Round to the nearest cent as needed.)
Trish invests 5,000 in her IRA in a bond trust that pays 7%  interest compounded quarterly. Sean invests 5,000 in his IRA in a certificate of deposit that pays 6.9%  compounded
continuously. Who has more money after 20 years,Trish or Sean?
After 20 years, Trish will have Ssquare . (Round to the nearest cent as needed.)

Solution
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Answer

After 20 years, Trish will have \19,348.50. Explanation 1. Calculate Trish's Investment Use the formula for compound interest: **\( A = P \left(1 + \frac{r}{n}\right)^{nt} \)**. Here, ( P = 5000 ), ( r = 0.07 ), ( n = 4 ), and ( t = 20 ). \( A = 5000 \left(1 + \frac{0.07}{4}\right)^{4 \times 20} \) \( A = 5000 \left(1 + 0.0175\right)^{80} \) \( A = 5000 \times (1.0175)^{80} \) \( A \approx 5000 \times 3.8697 \) \( A \approx 19348.50 \) 2. Calculate Sean's Investment Use the formula for continuous compounding: **\( A = Pe^{rt} \)**. Here, ( P = 5000 ), ( r = 0.069 ), and ( t = 20 ). \( A = 5000 \times e^{0.069 \times 20} \) \( A = 5000 \times e^{1.38} \) \( A \approx 5000 \times 3.9761 \) \( A \approx 19880.50 \)

Explanation

1. Calculate Trish's Investment<br /> Use the formula for compound interest: **\( A = P \left(1 + \frac{r}{n}\right)^{nt} \)**. Here, ( P = 5000 ), ( r = 0.07 ), ( n = 4 ), and ( t = 20 ).<br /> \( A = 5000 \left(1 + \frac{0.07}{4}\right)^{4 \times 20} \)<br /> \( A = 5000 \left(1 + 0.0175\right)^{80} \)<br /> \( A = 5000 \times (1.0175)^{80} \)<br /> \( A \approx 5000 \times 3.8697 \)<br /> \( A \approx 19348.50 \)<br /><br />2. Calculate Sean's Investment<br /> Use the formula for continuous compounding: **\( A = Pe^{rt} \)**. Here, ( P = 5000 ), ( r = 0.069 ), and ( t = 20 ).<br /> \( A = 5000 \times e^{0.069 \times 20} \)<br /> \( A = 5000 \times e^{1.38} \)<br /> \( A \approx 5000 \times 3.9761 \)<br /> \( A \approx 19880.50 \)
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