QuestionDecember 16, 2025

Tyee invested 440 in an account paying an interest rate of 8 8(3)/(8)% compounded continuously.Aria invested 440 in an account paying an interest rate of 8(3)/(4)% compounded daily. After 19 years . how much more money would Aria have in her account than Tyee, to the nearest dollar? Answer Attempt 1 out of 2 square

Tyee invested 440 in an account paying an interest rate of 8 8(3)/(8)% compounded continuously.Aria invested 440 in an account paying an interest rate of 8(3)/(4)% compounded daily. After 19 years . how much more money would Aria have in her account than Tyee, to the nearest dollar? Answer Attempt 1 out of 2 square
Tyee invested 440 in an account paying an
interest rate of 8 8(3)/(8)%  compounded
continuously.Aria invested 440 in an
account paying an interest rate of 8(3)/(4)% 
compounded daily. After 19 years . how much
more money would Aria have in her account
than Tyee, to the nearest dollar?
Answer
Attempt 1 out of 2
 square

Solution
4.1(259 votes)

Answer

\38 Explanation 1. Convert interest rates to decimals 8\frac{3}{8}\% = 8.375\% = 0.08375; 8\frac{3}{4}\% = 8.75\% = 0.0875 2. Calculate Tyee's final amount (continuous compounding) Use A = Pe^{rt}; P = 440, r = 0.08375, t = 19 A_T = 440 \times e^{0.08375 \times 19} A_T = 440 \times e^{1.59125} \approx 440 \times 4.9096 \approx 2160.22 3. Calculate Aria's final amount (daily compounding) Use A = P(1 + \frac{r}{n})^{nt}; n = 365, r = 0.0875, t = 19 A_A = 440 \times (1 + \frac{0.0875}{365})^{365 \times 19} A_A = 440 \times (1.000239726)^{6935} \approx 440 \times 4.9957 \approx 2198.11 4. Find the difference 2198.11 - 2160.22 = 37.89

Explanation

1. Convert interest rates to decimals<br /> $8\frac{3}{8}\% = 8.375\% = 0.08375$; $8\frac{3}{4}\% = 8.75\% = 0.0875$<br />2. Calculate Tyee's final amount (continuous compounding)<br /> Use $A = Pe^{rt}$; $P = 440$, $r = 0.08375$, $t = 19$<br /> $A_T = 440 \times e^{0.08375 \times 19}$<br /> $A_T = 440 \times e^{1.59125} \approx 440 \times 4.9096 \approx 2160.22$<br />3. Calculate Aria's final amount (daily compounding)<br /> Use $A = P(1 + \frac{r}{n})^{nt}$; $n = 365$, $r = 0.0875$, $t = 19$<br /> $A_A = 440 \times (1 + \frac{0.0875}{365})^{365 \times 19}$<br /> $A_A = 440 \times (1.000239726)^{6935} \approx 440 \times 4.9957 \approx 2198.11$<br />4. Find the difference<br /> $2198.11 - 2160.22 = 37.89$
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