Mary Ann will prefer Account 1
The use of "Compounding interest rate," which involves adding interest to the deposit's principal amount, is the main topic of discussion here.
Mary Ann's balance from account 2 over 3.7 years is $6,261.37
The below calculation is to derive maturity and value when an annual rate of 5.5% is applied.
Principal = $5,100
Annual rate = 5.5% 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.
In conclusion, the accrued value she will get years one year for this account is $5,568.70,
When the amount compounds continuously at a rate of 3.4% per year, the maturity value is determined by the calculation below.
Principal = $5,400
Annual rate = 3.4% continuously
A = P.e^rt where n=1
A = 5,400 * e^(0.04*1)
A = 5,400 * 1.04081077419
A = 5620.378180626
A = $5,620.39.
In conclusion, the accrued value she will greater one year for this account is $5,620.39.
Referring to how much would Mary Ann's balance be from Account 2 over 3.7 years. It is calculated as follows:
Annual rate = 3.4% 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
Therefore, the accrued value she will get after 3.7 years for this account is $6,261.37
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