Question

A 20,000 deposit earns 4.8 interest for 4 years . What is the final account balance if the interest is compounded semiannually ? Quarterly? Monthly ?

Answer 1

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