Answer:
$22,089.59
Explanation:
1st Year:
A = P [1 + (r / n)]ⁿᵇ
Where;
Amount Invested = P = $20,000
Interest Rate = r = 5.5% = 0.055
Compounded Quarterly = n = 4
Time = b = 1 year
Hence, by putting in the values above we can find the final amount in 1st year as;
A = $20,000 [1 + (0.055 / 4)]⁴ ˣ ¹
A = $20,000 [1+ 0.01375]⁴
A = $20,000 [1.01375]⁴
A = $20,000 x 1.056145
A = $21,122.90
2nd Year:
A = P [1 + (r / n)]ⁿᵇ
Now;
Investment from 1st year = P = $21,122.90
Interest Rate = r = 4.5% = 0.045
Compounded Quarterly = n = 4
Time = b = 1 Year
Hence by putting in the values above we get;
A = $21,122.90 [1 + (0.045 / 4)]⁴ ˣ ¹
A = $21,122.90 [1 + 0.01125]⁴
A = $21,122.90 [1.01125]⁴
A = $21,122.90 x 1.045765
A = $22,089.59
Hence the amount in the account in the 2nd year will be $22,089.59.