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DochEvi [55]
3 years ago
11

An initial deposit of $45,000 grows at an annual rate of 10% for 20 years. Compare the final balances resulting from continuous

compounding and annual compounding. (Round your answers to the nearest cent.)
Mathematics
1 answer:
Ugo [173]3 years ago
4 0

Answer:

Annual:         $302 737.50

Continuous: $332 507.52

Step-by-step explanation:

A. Compounded annually

The formula for <em>compound interest</em> is

A = P(1 + r)ⁿ

Data:

P = $45 000

r  = 10 %

t = 20 yr

Calculations:

n = 20

A = 45 000(1+ 0.10)²⁰

  = 45 000 × 1.10²⁰

  = 45 000 × 6.727 499 95

  = $302 737.50

B. Compounded continuously

The formula for <em>continuously compounded inerest</em> is

A = Pe^{rt}

A = 45 000e^{0.10 \times20}

= 45 000e^{2.0}

  = 45 000 × 7.389 056 61

  = $332 507.52

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