Tyra has recently inherited $5400, which she wants to deposit into an IRA account. She has determined that her two best bets are an account that compounds semi- annually at an annual rate of 3.1 % (Account 1) and an account that compounds continuously at an annual rate of 4 % (Account 2).
Step 2 of 2: How much would Tyra's balance be from Account 2 over 3.7 years? Round to two decimal places.

Tyra will definitely prefer the Account 2 over the Account 1

Tyra balance from account 2 over 3.7 years is $6,261.37

Explanation

She has determined that her two best bets are:

a. First account, which is at an annual rate of 3.1 %

b. Second account, which compounds continuously at an annual rate of 4%

Step 1

Account 1

Principal = $5,400

Annual rate = 3.1% semi-annually for 1 years

A = P(1+r/m)^n*t where n=1, t=2

A = 5,400*(1 + 0.031/2)^1*2

A = 5,400*(1.0155)^2

A = 5,400*1.03124025

A = 5568.69735

A = $5,568.70. So, the accrued value she will get after one years for this account is $5,568.70,

Account 2

Principal = $5,400

Annual rate = 4% continuously

A = P.e^rt where n=1

A = 5,400 * e^(0.04*1)

A = 5,400 * 1.04081077419

A = 5620.378180626

A = 5620.378180626

A = $5,620.39. So, the accrued value she will get after one years for this account is $5,620.39.

Conclusion: The second account will give a higher value than the first account.

Step 2

Annual rate = 4% continuously

A = P.e^rt where n=3.7

A = 5,400 * e^(0.04*3.7)

A = 5,400 * e^0.148

A = 5,400 * 1.15951289636

A = 6261.369640344

A = $6,261.37

The accrued value she will get after 3.7 years for this account is $6,261.37