Two years after Michelle deposited $25 000 in a TD Bank savings account that earned interest at 2.25% compounded monthly, the rate of interest was changed to 5.75% compounded semi-annually. How much was in the account fifteen years after the deposit was made?
A) $26149.59
B) $54641.30
C) $61201.27
D) $58510.72
E) $54629.87

Question

Quizplus · Accepted Answer

To calculate the total amount in the account after fifteen years, we need to break the calculation into two periods due to the change in interest rate and compounding frequency. First period (2 years with 2.25% interest compounded monthly):- Formula: A = P(1 + r/n)^(nt)- P = $25,000, r = 2.25% or 0.0225, n = 12 (monthly), t = 2 years- A = 25000(1 + 0.0225/12)^(12*2) ≈ $26,149.59Second period (remaining 13 years with 5.75% interest compounded semi-annually):- New P = $26,149.59 (amount from the first period), r = 5.75% or 0.0575, n = 2 (semi-annually), t = 13 years- A = 26149.59(1 + 0.0575/2)^(2*13) ≈ $54,641.30Therefore, the total amount in the account after fifteen years is approximately $54,641.30, which corresponds to option B.

Two Years After Michelle Deposited $25 000 in a TD