Question

Tyee invested $440 in an account paying an interest rate of 8 % compounded continuously. Aria invested $440 in an account paying an interest rate of 83% compounded daily. After 19 years, how much more money would Aria have in her account than Tyee, to the nearest dollar?​

Answer 1

We can start by using the formula for continuous compounding:

A = Pe^(rt)

where A is the amount of money in the account after t years, P is the principal invested, e is the constant 2.71828..., r is the interest rate, and t is the time in years.

For Tyee's account, we have:

A = 440*e^(0.08*19)
A = 440*e^1.52
A = 440*4.586
A = 2017.04

So after 19 years, Tyee would have $2017.04 in her account.

For Aria's account, we have:

A = 440*(1 + 0.83/365)^(365*19)
A = 440*1.0417^6935
A = 440*51.692
A = 22703.68

So after 19 years, Aria would have $22703.68 in her account.

The difference between the two accounts is:

22703.68 - 2017.04 = 20686.64

Therefore, to the nearest dollar, Aria would have $20,687 more in her account than Tyee after 19 years.

I hope this is right!

Answer 2

After 19 years, Aria would have approximately $650 more in her account than Tyee.

Step-by-step explanation:

To determine the future values of Tyee's and Aria's investments, we can use the compound interest formula. For continuously compounded interest, the formula is given by
`\(A_t = P \cdot e^(rt)\),`where
`\(A_t\)`is the future value,P is the principal amount, ris the interest rate, and t is time.

1. Tyee's Investment:

For Tyee's investment with an 8% continuous interest rate, the future value
`\(A_t\)` is calculated as
`\(A_t = 440 \cdot e^(0.08 \cdot 19)\).`

2. Aria's Investment:

For Aria's investment with an 8.3% daily compounded interest rate, the future value
`\(A_t\)` is calculated as
`\(A_t = 440 \cdot (1 + 0.083/365)^(365 \cdot 19)\).`

3. Subtract Tyee's future value from Aria's future value to find the difference, which is approximately $650 after rounding to the nearest dollar.

The calculations involve the use of the mathematical constant e and daily compounding for Aria's investment, resulting in the difference in their future values after 19 years.