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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 ?

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Answer:

Semi-annually: A = $24 178.51

Quarterly: A = $24 205.73

Monthly: A = $24 224.13

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

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