Answer:
Semi-annually: A = $24 178.51
Quarterly: A = $24 205.73
Monthly: A = $24 224.13
Step-by-step explanation:
The formula for compound interest is
A = P(1 + r)ⁿ
A. Compounded semi-annually
Data:
P = $20 000
APR = 4.8 %
t = 4 yr
Calculations:
n = 4 × 2 = 8
r = 0.048/2 = 0.024
A = 20 000(1+ 0.024)⁸
= 20 000 × 1.024⁸
= 20 000 × 1.208 926
= $24 178.51
B. Compounded Quarterly
n = 4 × 4 = 16
r = 0.048/4 = 0.012
A = 20 000(1+ 0.012)¹⁶
= 20 000 × 1.012¹⁶
= 20 000 × 1.210 286
= $24 205.73
C. Compounded monthly
n = 4 × 12 = 48
r = 0.048/12 = 0.004
A = 20 000(1+ 0.004)⁴⁸
= 20 000 × 1.004⁴⁸
= 20 000 × 1.211 207
= $24 224.13
